This document discusses edge-neighbor-rupture degree, a measure of vulnerability and reliability in communication networks. It defines edge-neighbor-rupture degree mathematically and provides examples of calculating it for different graphs. The main results are theorems about how edge-neighbor-rupture degree changes under common graph operations like joining graphs, adding vertices (thorny graphs), and taking unions of graphs. Edge-neighbor-rupture degree either increases or stays the same under these operations.
Numerical solution of a system of linear equations by
1) LU FACTORIZATION METHOD.
2) GAUSS ELIMINATION METHOD.
3) MATRIX INVERSION BY GAUSS ELIMINATION METHOD.
Introductory Mathematical Analysis for Business Economics International 13th ...Leblancer
Full download : http://alibabadownload.com/product/introductory-mathematical-analysis-for-business-economics-international-13th-edition-haeussler-test-bank/ Introductory Mathematical Analysis for Business Economics International 13th Edition Haeussler Test Bank
In [1] Abdel-Aal has introduced the notions of m-shadow graphs and n-splitting graphs, for all m, n ³ 1.
In this paper, we prove that, the m-shadow graphs for paths and complete bipartite graphs are odd
harmonious graphs for allm³ 1. Also, we prove the n-splitting graphs for paths, stars and symmetric
product between paths and null graphs are odd harmonious graphs for all n³ 1. In addition, we present
some examples to illustrate the proposed theories. Moreover, we show that some families of graphs admit
odd harmonious libeling.
system of algebraic equation by Iteration methodAkhtar Kamal
solve the system of algebraic equation by Iteration method
classification of Iteration method:-
(1) Jacobi's method
(2) Gauss-Seidel method
each problem
Numerical solution of a system of linear equations by
1) LU FACTORIZATION METHOD.
2) GAUSS ELIMINATION METHOD.
3) MATRIX INVERSION BY GAUSS ELIMINATION METHOD.
Introductory Mathematical Analysis for Business Economics International 13th ...Leblancer
Full download : http://alibabadownload.com/product/introductory-mathematical-analysis-for-business-economics-international-13th-edition-haeussler-test-bank/ Introductory Mathematical Analysis for Business Economics International 13th Edition Haeussler Test Bank
In [1] Abdel-Aal has introduced the notions of m-shadow graphs and n-splitting graphs, for all m, n ³ 1.
In this paper, we prove that, the m-shadow graphs for paths and complete bipartite graphs are odd
harmonious graphs for allm³ 1. Also, we prove the n-splitting graphs for paths, stars and symmetric
product between paths and null graphs are odd harmonious graphs for all n³ 1. In addition, we present
some examples to illustrate the proposed theories. Moreover, we show that some families of graphs admit
odd harmonious libeling.
system of algebraic equation by Iteration methodAkhtar Kamal
solve the system of algebraic equation by Iteration method
classification of Iteration method:-
(1) Jacobi's method
(2) Gauss-Seidel method
each problem
A graph with n vertex and m edges is said to be cubic graceful labeling if its vertices are labeled with distinct integers {0,1,2,3,……..,m3} such that for each edge f*( uv) induces edge mappings are {13,23,33,……,m3}. A graph admits a cubic graceful labeling is called a cubic graceful graph. In this paper, we proved that < K1,a , K1,b , K1c , K1,d>, associate urp with u(r+1)1 of K1,P, fixed vertices vr and ur of two copies of Pn are cubic graceful.
Module 5 (Part 3-Revised)-Functions and Relations.pdfGaleJean
The Cavite Mutiny of 1872 was an uprising of military personnel of Fort San Felipe, the Spanish arsenal in Cavite, Philippines on January 20, 1872, about 200 Filipino military personnel of Fort San Felipe Arsenal in Cavite, Philippines, staged a mutiny which in a way led to the Philippine Revolution in 1896. The 1872 Cavite Mutiny was precipitated by the removal of long-standing personal benefits to the workers such as tax (tribute) and forced labor exemptions on order from the Governor General Rafael de Izquierdo. Many scholars believe that the Cavite Mutiny of 1872 was the beginning of Filipino nationalism that would eventually lead to the Philippine Revolution of 1896.
DISTANCE TWO LABELING FOR MULTI-STOREY GRAPHSgraphhoc
An L (2, 1)-labeling of a graph G (also called distance two labeling) is a function f from the vertex set V (G) to the non negative integers {0,1,…, k }such that |f(x)-f(y)| ≥2 if d(x, y) =1 and | f(x)- f(y)| ≥1 if d(x, y) =2. The L (2, 1)-labeling number λ (G) or span of G is the smallest k such that there is a f with
max {f (v) : vє V(G)}= k. In this paper we introduce a new type of graph called multi-storey graph. The distance two labeling of multi-storey of path, cycle, Star graph, Grid, Planar graph with maximal edges and its span value is determined. Further maximum upper bound span value for Multi-storey of simple
graph are discussed.
In [8] Liang and Bai have shown that the kC4 − snake graph is an odd harmonious graph for each k ≥ 1. In this paper we generalize this result on cycles by showing that the kCn − snake with string 1,1,…,1 when n ≡ 0 (mod 4) are odd harmonious graph. Also we show that the kC4 − snake with m-pendant edges for each k,m ≥ 1 , (for linear case and for general case). Moreover, we show that, all subdivision of 2 m∆k - snake are odd harmonious for each k,m ≥ 1 . Finally we present some examples to illustrate the proposed theories.
An Algorithm for Odd Graceful Labeling of the Union of Paths and Cycles graphhoc
In 1991, Gnanajothi [4] proved that the path graph n
P with n vertex and n −1edge is odd graceful, and
the cycle graph Cm with m vertex and m edges is odd graceful if and only if m even, she proved the
cycle graph is not graceful if m odd. In this paper, firstly, we studied the graphCm∪Pn when m = 4, 6,8,10
and then we proved that the graphCm∪Pn
is odd graceful if m is even. Finally, we described an
algorithm to label the vertices and the edges of the vertex set ( ) m n
V C ∪P and the edge set ( ) m n
E C ∪P .
OPTIMIZING SIMILARITY THRESHOLD FOR ABSTRACT SIMILARITY METRIC IN SPEECH DIAR...mathsjournal
Speaker diarization is a critical task in speech processing that aims to identify "who spoke when?" in an
audio or video recording that contains unknown amounts of speech from unknown speakers and unknown
number of speakers. Diarization has numerous applications in speech recognition, speaker identification,
and automatic captioning. Supervised and unsupervised algorithms are used to address speaker diarization
problems, but providing exhaustive labeling for the training dataset can become costly in supervised
learning, while accuracy can be compromised when using unsupervised approaches. This paper presents a
novel approach to speaker diarization, which defines loosely labeled data and employs x-vector embedding
and a formalized approach for threshold searching with a given abstract similarity metric to cluster
temporal segments into unique user segments. The proposed algorithm uses concepts of graph theory,
matrix algebra, and genetic algorithm to formulate and solve the optimization problem. Additionally, the
algorithm is applied to English, Spanish, and Chinese audios, and the performance is evaluated using wellknown similarity metrics. The results demonstrate that the robustness of the proposed approach. The
findings of this research have significant implications for speech processing, speaker identification
including those with tonal differences. The proposed method offers a practical and efficient solution for
speaker diarization in real-world scenarios where there are labeling time and cost constraints.
A POSSIBLE RESOLUTION TO HILBERT’S FIRST PROBLEM BY APPLYING CANTOR’S DIAGONA...mathsjournal
We present herein a new approach to the Continuum hypothesis CH. We will employ a string conditioning,
a technique that limits the range of a string over some of its sub-domains for forming subsets K of R. We
will prove that these are well defined and in fact proper subsets of R by making use of Cantor’s Diagonal
argument in its original form to establish the cardinality of K between that of (N,R) respectively
A Positive Integer 𝑵 Such That 𝒑𝒏 + 𝒑𝒏+𝟑 ~ 𝒑𝒏+𝟏 + 𝒑𝒏+𝟐 For All 𝒏 ≥ 𝑵mathsjournal
According to Bertrand's postulate, we have 𝑝𝑛 + 𝑝𝑛 ≥ 𝑝𝑛+1. Is it true that for all 𝑛 > 1 then 𝑝𝑛−1 + 𝑝𝑛 ≥𝑝𝑛+1? Then 𝑝𝑛 + 𝑝𝑛+3 > 𝑝𝑛+1 + 𝑝𝑛+2where 𝑛 ≥ 𝑁, 𝑁 is a large enough value?
A POSSIBLE RESOLUTION TO HILBERT’S FIRST PROBLEM BY APPLYING CANTOR’S DIAGONA...mathsjournal
We present herein a new approach to the Continuum hypothesis CH. We will employ a string conditioning,
a technique that limits the range of a string over some of its sub-domains for forming subsets K of R. We
will prove that these are well defined and in fact proper subsets of R by making use of Cantor’s Diagonal
argument in its original form to establish the cardinality of K between that of (N,R) respectively.
Moving Target Detection Using CA, SO and GO-CFAR detectors in Nonhomogeneous ...mathsjournal
systems in complex situations. A fundamental problem in radar systems is to automatically detect targets while maintaining a
desired constant false alarm probability. This work studies two detection approaches, the first with a fixed threshold and the
other with an adaptive one. In the latter, we have learned the three types of detectors CA, SO, and GO-CFAR. This research
aims to apply intelligent techniques to improve detection performance in a nonhomogeneous environment using standard
CFAR detectors. The objective is to maintain the false alarm probability and enhance target detection by combining
intelligent techniques. With these objectives in mind, implementing standard CFAR detectors is applied to nonhomogeneous
environment data. The primary focus is understanding the reason for the false detection when applying standard CFAR
detectors in a nonhomogeneous environment and how to avoid it using intelligent approaches.
OPTIMIZING SIMILARITY THRESHOLD FOR ABSTRACT SIMILARITY METRIC IN SPEECH DIAR...mathsjournal
Speaker diarization is a critical task in speech processing that aims to identify "who spoke when?" in an
audio or video recording that contains unknown amounts of speech from unknown speakers and unknown
number of speakers. Diarization has numerous applications in speech recognition, speaker identification,
and automatic captioning. Supervised and unsupervised algorithms are used to address speaker diarization
problems, but providing exhaustive labeling for the training dataset can become costly in supervised
learning, while accuracy can be compromised when using unsupervised approaches. This paper presents a
novel approach to speaker diarization, which defines loosely labeled data and employs x-vector embedding
and a formalized approach for threshold searching with a given abstract similarity metric to cluster
temporal segments into unique user segments. The proposed algorithm uses concepts of graph theory,
matrix algebra, and genetic algorithm to formulate and solve the optimization problem. Additionally, the
algorithm is applied to English, Spanish, and Chinese audios, and the performance is evaluated using wellknown similarity metrics. The results demonstrate that the robustness of the proposed approach. The
findings of this research have significant implications for speech processing, speaker identification
including those with tonal differences. The proposed method offers a practical and efficient solution for
speaker diarization in real-world scenarios where there are labeling time and cost constraints.
The Impact of Allee Effect on a Predator-Prey Model with Holling Type II Func...mathsjournal
There is currently much interest in predator–prey models across a variety of bioscientific disciplines. The focus is on quantifying predator–prey interactions, and this quantification is being formulated especially as regards climate change. In this article, a stability analysis is used to analyse the behaviour of a general two-species model with respect to the Allee effect (on the growth rate and nutrient limitation level of the prey population). We present a description of the local and non-local interaction stability of the model and detail the types of bifurcation which arise, proving that there is a Hopf bifurcation in the Allee effect module. A stable periodic oscillation was encountered which was due to the Allee effect on the
prey species. As a result of this, the positive equilibrium of the model could change from stable to unstable and then back to stable, as the strength of the Allee effect (or the ‘handling’ time taken by predators when predating) increased continuously from zero. Hopf bifurcation has arose yield some complex patterns that have not been observed previously in predator-prey models, and these, at the same time, reflect long term behaviours. These findings have significant implications for ecological studies, not least with respect to examining the mobility of the two species involved in the non-local domain using Turing instability. A spiral generated by local interaction (reflecting the instability that forms even when an infinitely large
carrying capacity is assumed) is used in the model.
A POSSIBLE RESOLUTION TO HILBERT’S FIRST PROBLEM BY APPLYING CANTOR’S DIAGONA...mathsjournal
We present herein a new approach to the Continuum hypothesis CH. We will employ a string conditioning,a technique that limits the range of a string over some of its sub-domains for forming subsets K of R. We will prove that these are well defined and in fact proper subsets of R by making use of Cantor’s Diagonal argument in its original form to establish the cardinality of K between that of (N,R) respectively.
Moving Target Detection Using CA, SO and GO-CFAR detectors in Nonhomogeneous ...mathsjournal
Modernization of radar technology and improved signal processing techniques are necessary to improve detection systems in complex situations. A fundamental problem in radar systems is to automatically detect targets while maintaining a
desired constant false alarm probability. This work studies two detection approaches, the first with a fixed threshold and the
other with an adaptive one. In the latter, we have learned the three types of detectors CA, SO, and GO-CFAR. This research
aims to apply intelligent techniques to improve detection performance in a nonhomogeneous environment using standard
CFAR detectors. The objective is to maintain the false alarm probability and enhance target detection by combining
intelligent techniques. With these objectives in mind, implementing standard CFAR detectors is applied to nonhomogeneous
environment data. The primary focus is understanding the reason for the false detection when applying standard CFAR
detectors in a nonhomogeneous environment and how to avoid it using intelligent approaches
OPTIMIZING SIMILARITY THRESHOLD FOR ABSTRACT SIMILARITY METRIC IN SPEECH DIAR...mathsjournal
Speaker diarization is a critical task in speech processing that aims to identify "who spoke when?" in an
audio or video recording that contains unknown amounts of speech from unknown speakers and unknown
number of speakers. Diarization has numerous applications in speech recognition, speaker identification,
and automatic captioning. Supervised and unsupervised algorithms are used to address speaker diarization
problems, but providing exhaustive labeling for the training dataset can become costly in supervised
learning, while accuracy can be compromised when using unsupervised approaches. This paper presents a
novel approach to speaker diarization, which defines loosely labeled data and employs x-vector embedding
and a formalized approach for threshold searching with a given abstract similarity metric to cluster
temporal segments into unique user segments. The proposed algorithm uses concepts of graph theory,
matrix algebra, and genetic algorithm to formulate and solve the optimization problem. Additionally, the
algorithm is applied to English, Spanish, and Chinese audios, and the performance is evaluated using wellknown similarity metrics. The results demonstrate that the robustness of the proposed approach. The
findings of this research have significant implications for speech processing, speaker identification
including those with tonal differences. The proposed method offers a practical and efficient solution for
speaker diarization in real-world scenarios where there are labeling time and cost constraints
Modified Alpha-Rooting Color Image Enhancement Method on the Two Side 2-D Qua...mathsjournal
Color in an image is resolved to 3 or 4 color components and 2-Dimages of these components are stored in separate channels. Most of the color image enhancement algorithms are applied channel-by-channel on each image. But such a system of color image processing is not processing the original color. When a color image is represented as a quaternion image, processing is done in original colors. This paper proposes an implementation of the quaternion approach of enhancement algorithm for enhancing color images and is referred as the modified alpha-rooting by the two-dimensional quaternion discrete Fourier transform (2-D QDFT). Enhancement results of this proposed method are compared with the channel-by-channel image enhancement by the 2-D DFT. Enhancements in color images are quantitatively measured by the color enhancement measure estimation (CEME), which allows for selecting optimum parameters for processing by thegenetic algorithm. Enhancement of color images by the quaternion based method allows for obtaining images which are closer to the genuine representation of the real original color.
An Application of Assignment Problem in Laptop Selection Problem Using MATLABmathsjournal
The assignment – selection problem used to find one-to- one match of given “Users” to “Laptops”, the main objective is to minimize the cost as per user requirement. This paper presents satisfactory solution for real assignment – Laptop selection problem using MATLAB coding.
The aim of this paper is to study the class of β-normal spaces. The relationships among s-normal spaces, pnormal spaces and β-normal spaces are investigated. Moreover, we study the forms of generalized β-closed
functions. We obtain characterizations of β-normal spaces, properties of the forms of generalized β-closed
functions and preservation theorems.
Cubic Response Surface Designs Using Bibd in Four Dimensionsmathsjournal
Response Surface Methodology (RSM) has applications in Chemical, Physical, Meteorological, Industrial and Biological fields. The estimation of slope response surface occurs frequently in practical situations for the experimenter. The rates of change of the response surface, like rates of change in the yield of crop to various fertilizers, to estimate the rates of change in chemical experiments etc. are of
interest. If the fit of second order response is inadequate for the design points, we continue the
experiment so as to fit a third order response surface. Higher order response surface designs are sometimes needed in Industrial and Meteorological applications. Gardiner et al (1959) introduced third order rotatable designs for exploring response surface. Anjaneyulu et al (1994-1995) constructed third order slope rotatable designs using doubly balanced incomplete block designs. Anjaneyulu et al (2001)
introduced third order slope rotatable designs using central composite type design points. Seshu babu et al (2011) studied modified construction of third order slope rotatable designs using central composite
designs. Seshu babu et al (2014) constructed TOSRD using BIBD. In view of wide applicability of third
order models in RSM and importance of slope rotatability, we introduce A Cubic Slope Rotatable Designs Using BIBD in four dimensions.
The caustic that occur in geodesics in space-times which are solutions to the gravitational field equations with the energy-momentum tensor satisfying the dominant energy condition can be circumvented if quantum variations are allowed. An action is developed such that the variation yields the field equations
and the geodesic condition, and its quantization provides a method for determining the extent of the wave packet around the classical path.
Approximate Analytical Solution of Non-Linear Boussinesq Equation for the Uns...mathsjournal
For one dimensional homogeneous, isotropic aquifer, without accretion the governing Boussinesq equation under Dupuit assumptions is a nonlinear partial differential equation. In the present paper approximate analytical solution of nonlinear Boussinesq equation is obtained using Homotopy perturbation transform method(HPTM). The solution is compared with the exact solution. The comparison shows that the HPTM is efficient, accurate and reliable. The analysis of two important aquifer
parameters namely viz. specific yield and hydraulic conductivity is studied to see the effects on the height of water table. The results resemble well with the physical phenomena.
Common Fixed Point Theorems in Compatible Mappings of Type (P*) of Generalize...mathsjournal
In this paper, we give some new definition of Compatible mappings of type (P), type (P-1) and type (P-2) in intuitionistic generalized fuzzy metric spaces and prove Common fixed point theorems for six mappings
under the conditions of compatible mappings of type (P-1) and type (P-2) in complete intuitionistic fuzzy
metric spaces. Our results intuitionistically fuzzify the result of Muthuraj and Pandiselvi [15]
Mathematics subject classifications: 45H10, 54H25
A Probabilistic Algorithm for Computation of Polynomial Greatest Common with ...mathsjournal
In the earlier work, Knuth present an algorithm to decrease the coefficient growth in the Euclidean algorithm of polynomials called subresultant algorithm. However, the output polynomials may have a small factor which can be removed. Then later, Brown of Bell Telephone Laboratories showed the subresultant in another way by adding a variant called 𝜏 and gave a way to compute the variant. Nevertheless, the way failed to determine every 𝜏 correctly.
In this paper, we will give a probabilistic algorithm to determine the variant 𝜏 correctly in most cases by adding a few steps instead of computing 𝑡(𝑥) when given 𝑓(𝑥) and𝑔(𝑥) ∈ ℤ[𝑥], where 𝑡(𝑥) satisfies that 𝑠(𝑥)𝑓(𝑥) + 𝑡(𝑥)𝑔(𝑥) = 𝑟(𝑥), here 𝑡(𝑥), 𝑠(𝑥) ∈ ℤ[𝑥]
Table of Contents - September 2022, Volume 9, Number 2/3mathsjournal
Applied Mathematics and Sciences: An International Journal (MathSJ ) aims to publish original research papers and survey articles on all areas of pure mathematics, theoretical applied mathematics, mathematical physics, theoretical mechanics, probability and mathematical statistics, and theoretical biology. All articles are fully refereed and are judged by their contribution to advancing the state of the science of mathematics.
Essentials of Automations: Optimizing FME Workflows with ParametersSafe Software
Are you looking to streamline your workflows and boost your projects’ efficiency? Do you find yourself searching for ways to add flexibility and control over your FME workflows? If so, you’re in the right place.
Join us for an insightful dive into the world of FME parameters, a critical element in optimizing workflow efficiency. This webinar marks the beginning of our three-part “Essentials of Automation” series. This first webinar is designed to equip you with the knowledge and skills to utilize parameters effectively: enhancing the flexibility, maintainability, and user control of your FME projects.
Here’s what you’ll gain:
- Essentials of FME Parameters: Understand the pivotal role of parameters, including Reader/Writer, Transformer, User, and FME Flow categories. Discover how they are the key to unlocking automation and optimization within your workflows.
- Practical Applications in FME Form: Delve into key user parameter types including choice, connections, and file URLs. Allow users to control how a workflow runs, making your workflows more reusable. Learn to import values and deliver the best user experience for your workflows while enhancing accuracy.
- Optimization Strategies in FME Flow: Explore the creation and strategic deployment of parameters in FME Flow, including the use of deployment and geometry parameters, to maximize workflow efficiency.
- Pro Tips for Success: Gain insights on parameterizing connections and leveraging new features like Conditional Visibility for clarity and simplicity.
We’ll wrap up with a glimpse into future webinars, followed by a Q&A session to address your specific questions surrounding this topic.
Don’t miss this opportunity to elevate your FME expertise and drive your projects to new heights of efficiency.
Connector Corner: Automate dynamic content and events by pushing a buttonDianaGray10
Here is something new! In our next Connector Corner webinar, we will demonstrate how you can use a single workflow to:
Create a campaign using Mailchimp with merge tags/fields
Send an interactive Slack channel message (using buttons)
Have the message received by managers and peers along with a test email for review
But there’s more:
In a second workflow supporting the same use case, you’ll see:
Your campaign sent to target colleagues for approval
If the “Approve” button is clicked, a Jira/Zendesk ticket is created for the marketing design team
But—if the “Reject” button is pushed, colleagues will be alerted via Slack message
Join us to learn more about this new, human-in-the-loop capability, brought to you by Integration Service connectors.
And...
Speakers:
Akshay Agnihotri, Product Manager
Charlie Greenberg, Host
Software Delivery At the Speed of AI: Inflectra Invests In AI-Powered QualityInflectra
In this insightful webinar, Inflectra explores how artificial intelligence (AI) is transforming software development and testing. Discover how AI-powered tools are revolutionizing every stage of the software development lifecycle (SDLC), from design and prototyping to testing, deployment, and monitoring.
Learn about:
• The Future of Testing: How AI is shifting testing towards verification, analysis, and higher-level skills, while reducing repetitive tasks.
• Test Automation: How AI-powered test case generation, optimization, and self-healing tests are making testing more efficient and effective.
• Visual Testing: Explore the emerging capabilities of AI in visual testing and how it's set to revolutionize UI verification.
• Inflectra's AI Solutions: See demonstrations of Inflectra's cutting-edge AI tools like the ChatGPT plugin and Azure Open AI platform, designed to streamline your testing process.
Whether you're a developer, tester, or QA professional, this webinar will give you valuable insights into how AI is shaping the future of software delivery.
Smart TV Buyer Insights Survey 2024 by 91mobiles.pdf91mobiles
91mobiles recently conducted a Smart TV Buyer Insights Survey in which we asked over 3,000 respondents about the TV they own, aspects they look at on a new TV, and their TV buying preferences.
UiPath Test Automation using UiPath Test Suite series, part 3DianaGray10
Welcome to UiPath Test Automation using UiPath Test Suite series part 3. In this session, we will cover desktop automation along with UI automation.
Topics covered:
UI automation Introduction,
UI automation Sample
Desktop automation flow
Pradeep Chinnala, Senior Consultant Automation Developer @WonderBotz and UiPath MVP
Deepak Rai, Automation Practice Lead, Boundaryless Group and UiPath MVP
DevOps and Testing slides at DASA ConnectKari Kakkonen
My and Rik Marselis slides at 30.5.2024 DASA Connect conference. We discuss about what is testing, then what is agile testing and finally what is Testing in DevOps. Finally we had lovely workshop with the participants trying to find out different ways to think about quality and testing in different parts of the DevOps infinity loop.
Key Trends Shaping the Future of Infrastructure.pdfCheryl Hung
Keynote at DIGIT West Expo, Glasgow on 29 May 2024.
Cheryl Hung, ochery.com
Sr Director, Infrastructure Ecosystem, Arm.
The key trends across hardware, cloud and open-source; exploring how these areas are likely to mature and develop over the short and long-term, and then considering how organisations can position themselves to adapt and thrive.
Neuro-symbolic is not enough, we need neuro-*semantic*Frank van Harmelen
Neuro-symbolic (NeSy) AI is on the rise. However, simply machine learning on just any symbolic structure is not sufficient to really harvest the gains of NeSy. These will only be gained when the symbolic structures have an actual semantics. I give an operational definition of semantics as “predictable inference”.
All of this illustrated with link prediction over knowledge graphs, but the argument is general.
The Art of the Pitch: WordPress Relationships and SalesLaura Byrne
Clients don’t know what they don’t know. What web solutions are right for them? How does WordPress come into the picture? How do you make sure you understand scope and timeline? What do you do if sometime changes?
All these questions and more will be explored as we talk about matching clients’ needs with what your agency offers without pulling teeth or pulling your hair out. Practical tips, and strategies for successful relationship building that leads to closing the deal.
GDG Cloud Southlake #33: Boule & Rebala: Effective AppSec in SDLC using Deplo...James Anderson
Effective Application Security in Software Delivery lifecycle using Deployment Firewall and DBOM
The modern software delivery process (or the CI/CD process) includes many tools, distributed teams, open-source code, and cloud platforms. Constant focus on speed to release software to market, along with the traditional slow and manual security checks has caused gaps in continuous security as an important piece in the software supply chain. Today organizations feel more susceptible to external and internal cyber threats due to the vast attack surface in their applications supply chain and the lack of end-to-end governance and risk management.
The software team must secure its software delivery process to avoid vulnerability and security breaches. This needs to be achieved with existing tool chains and without extensive rework of the delivery processes. This talk will present strategies and techniques for providing visibility into the true risk of the existing vulnerabilities, preventing the introduction of security issues in the software, resolving vulnerabilities in production environments quickly, and capturing the deployment bill of materials (DBOM).
Speakers:
Bob Boule
Robert Boule is a technology enthusiast with PASSION for technology and making things work along with a knack for helping others understand how things work. He comes with around 20 years of solution engineering experience in application security, software continuous delivery, and SaaS platforms. He is known for his dynamic presentations in CI/CD and application security integrated in software delivery lifecycle.
Gopinath Rebala
Gopinath Rebala is the CTO of OpsMx, where he has overall responsibility for the machine learning and data processing architectures for Secure Software Delivery. Gopi also has a strong connection with our customers, leading design and architecture for strategic implementations. Gopi is a frequent speaker and well-known leader in continuous delivery and integrating security into software delivery.
FIDO Alliance Osaka Seminar: The WebAuthn API and Discoverable Credentials.pdf
EDGE-NEIGHBOR RUPTURE DEGREE ON GRAPH OPERATIONS
1. Applied Mathematics and Sciences: An International Journal (MathSJ ), Vol. 5, No. 1/2/3, September 2018
DOI : 10.5121/mathsj.2018.5301 1
EDGE-NEIGHBOR RUPTURE DEGREE ON GRAPH
OPERATIONS
Saadet Eskiizmirliler 1
, Zeynep Örs Yorgan cioğlu2
, Refet Polat3
And Mehmet Ümit Gürsoy4
1,3
Department of Mathematics, Faculty of Science, Yasar University, Izmir, Turkey,
2
Maritime and Port Management Program, Vocational School,
Yasar University, Izmir, Turkey,
4
Izmir, Turkey,
ABSTRACT
Vulnerability and reliability parameters measure the resistance of the network to disruption of operation
after the failure of certain stations or communication links in a communication network. An edge
subversion strategy of a graph , say , is a set of edge(s) in whose adjacent vertices which is incident
with the removal edge(s) are removed from . The survival subgraph is denoted by − . The edge-
neighbor-rupture degree of connected graph , , is defined to be = − −
| | − − : ⊆ , − ≥ 1 where is any edge-cut-strategy of , − is the number
of the components of − , and − is the maximum order of the components of − . In this paper
we give some results for the edge-neighbor-rupture degree of the graph operations and Thorny graph types
are examined.
KEYWORDS
Edge-neighbor-rupture degree, Thorny graphs, Vulnerability, Reliability.
1. INTRODUCTION
A communication network can be brokedown to pieces partially or completely from unexpected
factors. This situation can prevent data transmit so there would be a big problem on the system to
perform it’s task. Therefore, the vulnerability and the reliability measure the resistance of the
network disturbance of operations after the failure of certain stations. To measure the
vulnerability and the reliability we have some parameters which are connectivity [7,11,12],
integrity [3], scattering number [8], rupture degree [9], neighbor-rupture degree [1] and edge-
neighbor-rupture degree [2].
Terminology and notations are not defined in this paper but it can be found [4,5]. Let =
, be a simple graph and let e be any edge of . The set,
= ∈ | ≠ ; ! " is the open neighborhood of e, and [e] = {e}
∪ (e) is the closed neighborhood of e. An edge e in is said to be subverted if the closed
neighborhood of e is removed from . In other words, if = $, % than − &e( = − $, % . A
set of edges = ), *, … , , is called an edge subversion strategy of if each of the edges in
has been subverted from . If has been subverted from the graph , then the remaining graph is
called survival graph, denoted by − . An edge subversion strategy is called an edge-cut-
strategy of if the survival subgraph − is disconnected or is a single vertex or the empty graph
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2
[10]. is any edge-cut-strategy of , ( − ) is the number of the components of − , and
( − ) is the maximum order of the components of − .
The definition of edge-neighbor-rupture degree of a connected graph is
= − − | | − − : ⊆ , − ≥ 1 .
Definition 1.1: ∈ -
and ∀% ∈ V for each vertex of , if deg % = than is called r-
regular graph [4].
Definition 1.2: ) and * graphs have disjoint vertex sets ) and * and edge sets ) and *
respectively. The join operation of two ) and * graphs is denoted by ) + * and consist of
) ∪ *which is union of two ) and * graphs and all edges joining ) and *[4].
Definition 1.3:Let 3), 3*, … , 34be non-negative integers. The Thorny Graph of the graph , with
parameters3), 3*, … , 34,is obtained by attaching 35 new vertices of degree one to the vertex$5 of
the graph , 6 = 1,2, … , .
The Thorny graph of the graph is denoted by ⋆
, or if the respectiveparameters need to be
specified, by ⋆ 3), 3*, … , 34 [6].
Definition 1.4:Forthree or more disjoint graphs ), *, … , 4 , the sequential join
) + * + ⋯ + 4
is the graph
) + * ∪ * + : ∪ … ∪ 4;) + 4 [4].
Definition 1.5: Connectivity < is the minimum number of vertices that need to be removed in
order to disconnect a graph [4].
Definition 1.6: The integrity of a graph = , is defined by = = 6 | | + −
; ⊂ where − denotes the order of largest component in − [3].
Definition 1.7: The rupture degree of a non-complete connected graph is defined by =
− − | | − − : ⊂ , − ˃ 1 where − denotes the
number of components in the graph − and − is the order of the largest component of
− [9].
Definition 1.8: The neighbor integrity of a graph is defined by
= = 6 | | + ! − : ⊂ where is any vertex subversion strategy of and
! − is the order of the largest component of − [10].
Definition 1.9: The neighbor rupture degree of a non-complete connected graph is defined to
be = − − | | − ! − : ⊂ , − ≥ 1 where is any vertex
subversion strategy of , − is the number of connected components in − and
! − is the maximum order of the components of − [13].
Definition 1.10: The edge-neighbor-rupture degree of a connected graph is defined to be
= − − | | − − ∶ ⊆ , − ≥ 1 , where is any edge-
3. Applied Mathematics and Sciences: An International Journal (MathSJ ), Vol. 5, No. 1/2/3, September 2018
3
cut-strategy of , − is the number of the components of − , and − is the
maximum order of the components of − .
Example:Let's give an exampleof
the calculation of the edge-neighbor-
rupture-degree.
− = 1
| | = 0
− = 19
− − | | − −
= 1 − 0 − 19 = −18
Figure 1.1
− = 6
| | = 3
− = 7
− − | | − − = 6 − 3 − 7
= −4
Figure 1.2
− = 8
| | = 5
− = 2
− − | | − − = 8 − 5 − 2
= 1
Figure 1.3
− = 9
| | = 5
− = 1
− − | | − − = 9 − 5 − 1
= 3
Figure 1.4
− = 9
| | = 5
− = 1
− − | | − − = 9 − 5 −
1 = 3
Figure 1.5
4. Applied Mathematics and Sciences: An International Journal (MathSJ ), Vol. 5, No. 1/2/3, September 2018
4
As shown, figure 1.1, figure 1.2,figure 1.3,figure 1.4 and figure 1.5
= −18, −4,1,3,3
= 3.
In this paper, the edge-neighbor-rupture degree of some graphs is obtained and the relations
between edge-neighbor-rupture degree and other parameters are determined [2].
2. EDGE-NEIGHBOR-RUPTURE DEGREE ON GRAPH OPERATIONS
In this section some theorems are given for edge-neighbor-rupture degree on the graph
operations. Connected, undirected, simple graphs are examined.
Theorem 2.1:Let be a regular graph and ⋆
is a thorny graph of (adding a vertex to any
vertex of a graph). Then the edge-neighbor-rupture degree of is,
⋆
= + 1.
Proof:Since is regular graph, you can start from any edge to delete. There are two cases.
Case 1: If we start to delete an edge that is incident to an added vertex, while Sedge-cut-
strategynumber is not changing,( − ) numbers of components are increased 1. So the result is
increased 1.
Case 2:If we start to delete an edge that is not incident to an added vertex, while Sedge-cut-
strategy number and the number of the components are not changed, maximum order of the
components are increased. So the result is increased.
The result takes maximum value in case 1. So the proof is completed.■
Theorem 2.2: Edge-neighbor-rupture degree of thorny of regular graph (adding i vertices
equally to every vertex of a graph for1 ≤ 6 ≤ ) is,
⋆
= 6 − J
4
*
K − 1.
Proof: Let S be anedge-cut-strategyof ⋆
and let | | = . There are two cases for the elements of
.
Case 1: If 0 ≤ < J
4
*
K, then ⋆
− ≤ 2 6 + 1 and ⋆
− ≥ 6 + 1, so we have
⋆
− − | | − ⋆
− ≤ 2 6 + 1 − − 6 + 1 = 2 6 − − 6.
Let’s = 2 6 − − 6 . Since is an increasing function in 0 ≤ < J
4
*
K, it takes its maximum
value at MJ
4
*
K − 1N, and
MJ
2
K − 1N = 2 MJ
2
K − 1N 6 − J
2
K − 6.
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5
Thus we get ⋆
≤ 2 MJ
4
*
K − 1N 6 − J
4
*
K − 6 .
Case 2: If J
4
*
K ≤ ≤
:4P;4
*
, then ⋆
− ≤ 6and ⋆
− ≥ 1, so we have
⋆
− − | | − ⋆
− ≤ 6 − − 1.
Let’s = 6 − − 1.Since is a decreasing function in 0 ≤ < J
4
*
K, it takes its maximum
value at J
4
*
K, and MJ
4
*
KN = 6 − J
4
*
K − 1.
Thus we get ⋆
≤ 6 − J
4
*
K − 1.
From Case1 and Case 2 we have
⋆
≤ 6 − J
4
*
K − 1. (1)
There exist ∗
such that
= J
4
*
K, ⋆
− ∗
= 6 and ⋆
− ∗
= 1, thus we have
⋆ ≥ 6 − J
4
*
K − 1. (2)
From (1) and (2) we get
⋆
= 6 − J
4
*
K − 1. ■
Corollary 2.1: LetR4
⋆
is a Thorny graph of R4 (adding i vertices equally to every vertex of a
graph for2 ≤ 6 ≤ ). Then the edge-neighbor-rupture degree of R4
⋆
is,
R4
⋆
= 6 − J
4
*
K − 1.
Proof: It is the same as proof of Theorem 2.2 ■
Corollary 2.2: LetS4
⋆
is a Thorny graph of S4 (adding i vertices equally to every vertex of a
graph for2 ≤ 6 ≤ ). Then the edge-neighbor-rupture degree of S4
⋆
is,
S4
⋆
= 6 − J
4
*
K − 1.
Proof: It is the same as proof of Theorem 2.2. ■
Theorem 2.3: Edge-neighbor-rupture degree of Thorny graphof 4 is 6 ≥ 2 ,
4
⋆
= 6 − .
Proof: Let S be an edge-cut-strategyof 4
⋆
and let | | = . There are two cases for the elements of
.
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6
Case 1: If 0 ≤ < − 1, then 4
⋆
− ≤ 6 + 1 and 4
⋆
− ≥ 6 + 1, so we have
4
⋆
− − | | − 4
⋆
− ≤ 6 + 1 − − 6 + 1 = 6 − − 6.
Let = 6 − − 6 . Since is an increasing function in 0 ≤ < − 1, it takes its
maximum value − 2 and − 2 = − 2 6 − 1 − 6.
Thus we get 4
⋆
≤ 6 − − 36 + 2.
Case 2: If − 1 ≤ ≤ * + − 1 then 4
⋆ − ≤ 6 and 4
⋆ − ≥ 1, so we have
4
⋆
− − | | − 4
⋆
− ≤ 6 − − 1.
Let = 6 − − 1.Since is a decreasing function in − 1 ≤ ≤ *
+ − 1it takes its
maximum value at − 1 and
− 1 = 6 − + 1 − 1 = 6 − .
Thus we get 4
⋆
≤ 6 − .
From Case1 and Case 2 we have
4
⋆
≤ 6 − . (3)
There exist ∗
such that
= − 1, 4
⋆
− ∗
= 6 and 4
⋆
− ∗
= 1, thus we have
4
⋆
≥ 6 − . (4)
From (3) and (4) we get 4
⋆
= 6 − . ■
Theorem 2.4: Let R4,R, is a path of order and respectively. The edge-neighbor-rupture
degree of addition of R4 and R, is,
R4 + R, = T
R, −
2
, 6U %
R,;) − J
2
K , 6U V
W , <
Proof:
Case 1:If we select an edge-cut-strategy fromR4, we needed
4
*
edges to delete all the edges of R4
soR,is remained. Therefore,
R4 + R, = T
R, −
2
, 6U %
R,;) − J
2
K , 6U V
W
Case 2: If we select an edge-cut-strategy from combining edges of R4 and R,, We get,
R4 + R, = R,;4 − .
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7
Case 3:If we select an edge-cut-strategy fromR,, we need
4
*
edges to delete all the edges of
R,soR4 is remained. Therefore,
R4 + R, = T
R4 −
2
, 6U %
R4;) − J
2
K , 6U V
W
The results take maximum value in case 1. So the proof is completed.
Corollary 2.3: The edge-neighbor-rupture degree of R*+R4 is,
R* + R, = R4 − 1 .
Theorem 2.5: Let ), *, … , 4be connected graphs then,
) ∪ * ∪ … ∪ 4 ≥ ) + * + ⋯ + 4
Proof: Let = ) ∪ * ∪ … ∪ 4be union of ), *, … , 4. Let = ), *, … , 4 be an edge Nr-
set of ), *, … , 4 respectively and let = ) ∪ * ∪ … ∪ 4be an edge-subversion strategy of .
Then we obtain,
≥ − − | | − −
= & ) − ) + * − * + ⋯ + 4 − 4 ( − &| )| + | *| + ⋯ + | 4|(
− & ) − ) + * − * + ⋯ + 4 − 4 (
= ) − ) − | )| − ) − ) + * − * − | *| − * − * + ⋯ + 4 − 4
− | 4| − 4 − 4
) + * + ⋯ + 4 . ■
Theorem 2.6: Let be a connected graph, then the edge-neighbor-rupture degree of is,
≥ − X
2
Y.
Proof: For the minimum value of , − must be the smallest, | | and −
must be the greatest.
Let S be an edge-cut-strategy of and | | = . There are two cases for the elements of .
Case 1: If ≤ X
4;)
*
Ythen − = 1 and − ≥ − 2 .
So we have
− − | | − − ≤ 1 − − − 2 = 1 + − = .
This equality takes maximum value for = X
4;)
*
Y.
There are two conditions:
Case i: If n is odd;
8. Applied Mathematics and Sciences: An International Journal (MathSJ ), Vol. 5, No. 1/2/3, September 2018
8
= 1 +
− 1
2
− = −
− 1
2
= − X
2
Y.
Case ii: If n is even;
= 1 +
− 2
2
− = −
2
Case 2: If
4 4;)
*
> > X
4;)
*
Y then − ≤ 1and − ≥ 1.
− − | | − − ≤ 1 − − 1 = − .
This equality takes the maximum value for = X
4
*
Y.
From all cases, we obtain, ≥ − X
4
*
Y. ■
Corollary 2.4: Let be a connected graph, then the edge-neighbor-rupture degree of is,
− X
4
*
Y ≤ ≤ − 4.
Proof: From Theorem 2.6 and [2], the proof is complete. ■
3. COMPUTING EDGE-NEIGHBOR-RUPTURE DEGREE OF A GRAPH
In this section, an algorithm is proposed in order to calculate the edge-neighbor-rupture degreefor
any simple finite undirected graph without loops and multiple edges by using the findENR
function.
Algorithm Edge Neighbor Rupture (ENR)
Output: ENR value for given any graph G
Begin
ENR←-∞;
for all edge subsets [ ⊆ do
if findENR( , [)> ENRthen
ENR=findENR( , [);
end
end
end.
The function below,find ENR, returns the ENR value for the edge subset for the graph.
function findENR( , [);
Input: Graph , , edgesubset [
Output:ENR value for given an [edge subset of .
Begin
: vertex set incident with [ edges.
for all $ ∈ do
removeu from 6. . −
end
9. Applied Mathematics and Sciences: An International Journal (MathSJ ), Vol. 5, No. 1/2/3, September 2018
9
Componentnumber ← find the number of components of −
MaxCompVertexnum ← find the vertex number of maximum component of −
findENR←{Component number – number of ( [) – MaxCompVertexnum }
end
4. CONCLUSION
In this study, we investigate the edge-neighbor rupture degree of graphs obtained by graph
operations. The graph operations are used to obtain new graphs. Union, join and mostly thorny
operations are taken into consideration in this work. These operations are performed to various
graphs and their edge-neighbor rupture degrees were determined.
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AUTHORS
Saadet Eskiizmirliler She was graduated fromYaşar University Mathematics
department in 2010, she had got master degree in 2012 fromYaşar University Math
department and she has been doing doktorate at Yaşar University Math department
at applied mathematics since 2014. She has been working at Yasar University since
2014.
Zeynep Örs Yorgancioğlu She was graduated from Ege University Mathematics
department in 2003, she had got master degree in 2010 from Ege University Math
department and she had got Ph. D degree in 2015 from Ege University Math
department at applied Mathematics. She has been working at Yasar University
since 2007.
Refet Polat Achieved his BSc degree in mathematics majoring in computer science
at Ege University in 2000. He received his MSc and PhD degrees in applied
mathematics at Ege University in 2003 and 2009. His research interests focus on
applied mathematics, graph theory, ordinary differential equations, numerical
methods, and artificial intelligence in education
Mehmet Ümit Gürsoy He was graduated from Ege University Mathematics
department in 2000, he had got master degree in 2005 from Ege University Math
department and he had got Ph.D degree in 2014 from Ege University Math
department at applied mathematics.