Graph theory is the study of points and lines, and how sets of points called vertices can be connected by lines called edges. It involves types of graphs like regular graphs where each vertex has the same number of neighbors, and bipartite graphs where the vertices can be partitioned into two sets with no edges within each set. Graphs can be represented using adjacency matrices and adjacency lists. Basic graph algorithms include depth-first search, breadth-first search, and finding shortest paths between vertices. Graph coloring assigns colors to vertices so that no adjacent vertices have the same color.
In mathematics, graph theory is the study of graphs, which are mathematical structures used to model pairwise relations between objects.Graph theory is also important in real life.
In mathematics, graph theory is the study of graphs, which are mathematical structures used to model pairwise relations between objects.Graph theory is also important in real life.
what is Hamilton path and Euler path?
History of Euler path and Hamilton path
Vertex(node) and edge
Hamilton path and Hamilton circuit
Euler path and Euler circuit
Degree of vertex and comparison of Euler and Hamilton path
Solving a problem
what is Hamilton path and Euler path?
History of Euler path and Hamilton path
Vertex(node) and edge
Hamilton path and Hamilton circuit
Euler path and Euler circuit
Degree of vertex and comparison of Euler and Hamilton path
Solving a problem
introduction and representation of graph.
graph is collection of points and vertices.
there are 2 types of the graph 1. directed
2. undirected graph.
representation of graph 2 ways
Adjacency matrix
Adjacency list
Cosmetic shop management system project report.pdfKamal Acharya
Buying new cosmetic products is difficult. It can even be scary for those who have sensitive skin and are prone to skin trouble. The information needed to alleviate this problem is on the back of each product, but it's thought to interpret those ingredient lists unless you have a background in chemistry.
Instead of buying and hoping for the best, we can use data science to help us predict which products may be good fits for us. It includes various function programs to do the above mentioned tasks.
Data file handling has been effectively used in the program.
The automated cosmetic shop management system should deal with the automation of general workflow and administration process of the shop. The main processes of the system focus on customer's request where the system is able to search the most appropriate products and deliver it to the customers. It should help the employees to quickly identify the list of cosmetic product that have reached the minimum quantity and also keep a track of expired date for each cosmetic product. It should help the employees to find the rack number in which the product is placed.It is also Faster and more efficient way.
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Immunizing Image Classifiers Against Localized Adversary Attacksgerogepatton
This paper addresses the vulnerability of deep learning models, particularly convolutional neural networks
(CNN)s, to adversarial attacks and presents a proactive training technique designed to counter them. We
introduce a novel volumization algorithm, which transforms 2D images into 3D volumetric representations.
When combined with 3D convolution and deep curriculum learning optimization (CLO), itsignificantly improves
the immunity of models against localized universal attacks by up to 40%. We evaluate our proposed approach
using contemporary CNN architectures and the modified Canadian Institute for Advanced Research (CIFAR-10
and CIFAR-100) and ImageNet Large Scale Visual Recognition Challenge (ILSVRC12) datasets, showcasing
accuracy improvements over previous techniques. The results indicate that the combination of the volumetric
input and curriculum learning holds significant promise for mitigating adversarial attacks without necessitating
adversary training.
CFD Simulation of By-pass Flow in a HRSG module by R&R Consult.pptxR&R Consult
CFD analysis is incredibly effective at solving mysteries and improving the performance of complex systems!
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R&R and Tetra Engineering Group Inc. were asked to solve the issue with reduced steam production.
An inspection had shown that a significant amount of hot flue gas was bypassing the boiler tubes, where the heat was supposed to be transferred.
R&R Consult conducted a CFD analysis, which revealed that 6.3% of the flue gas was bypassing the boiler tubes without transferring heat. The analysis also showed that the flue gas was instead being directed along the sides of the boiler and between the modules that were supposed to capture the heat. This was the cause of the reduced performance.
Based on our results, Tetra Engineering installed covering plates to reduce the bypass flow. This improved the boiler's performance and increased electricity production.
It is always satisfying when we can help solve complex challenges like this. Do your systems also need a check-up or optimization? Give us a call!
Work done in cooperation with James Malloy and David Moelling from Tetra Engineering.
More examples of our work https://www.r-r-consult.dk/en/cases-en/
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Terzaghi's soil bearing capacity theory, developed by Karl Terzaghi, is a fundamental principle in geotechnical engineering used to determine the bearing capacity of shallow foundations. This theory provides a method to calculate the ultimate bearing capacity of soil, which is the maximum load per unit area that the soil can support without undergoing shear failure. The Calculation HTML Code included.
Water scarcity is the lack of fresh water resources to meet the standard water demand. There are two type of water scarcity. One is physical. The other is economic water scarcity.
Overview of the fundamental roles in Hydropower generation and the components involved in wider Electrical Engineering.
This paper presents the design and construction of hydroelectric dams from the hydrologist’s survey of the valley before construction, all aspects and involved disciplines, fluid dynamics, structural engineering, generation and mains frequency regulation to the very transmission of power through the network in the United Kingdom.
Author: Robbie Edward Sayers
Collaborators and co editors: Charlie Sims and Connor Healey.
(C) 2024 Robbie E. Sayers
2. Introduction
Graph Theory is the study of points and lines.
In particular, it involves the ways in which sets of
points, called vertices, can be connected by lines
called edges.
Graph Theory has proven useful in the design of
integrated circuits for computers and other
electronic devices.
Graph Theory was invented by Leonhard Euler.
3. Graphs And Basic Terminologies
A Graph is an ordered pair G = (V, E) comprising
a set V of vertices, nodes or points together with a
set E of edges, arcs or lines, which are 2-element subsets
of V.
An edge is associated with two vertices, and the
association takes the form of the unordered pair of the
vertices.
A Graph may be directed or undirected, weighted or
unweighted.
A Graph may be with self-loop or self-edge.
5. Types Of Graphs
Null Graph:
A Graph which contains only isolated nodes(i.e. set of edges of graph
is empty) is called as Null Graph.
Regular Graph:
A Graph in which each vertex has the same number of neighbours(i.e.
every vertex has the same degree) is called as Regular Graph.
A Regular Graph with vertices of degree K is called a K -Regular
Graph or regular graph of degree K.
Complete Graph:
A Complete Graph is a graph in which each pair of vertices is joined
by an edge.
A Complete Graph contains all possible edges.
6. Types Of Graphs
Bipartite Graph:
A Bipartite Graph is a graph in which the vertex set can
be partitioned into two sets, W and X, so that no two vertices
in W share a common edge and no two vertices in X share a common
edge.
Chromatic number of Bipartite Graph is 2.
Complete Bipartite Graph:
In a Complete Bipartite Graph, the vertex set is the union of two
disjoint sets, W and X, so that every vertex in W is adjacent to every
vertex in X but there are no edges within W or X.
7. Example Of Types Of Graphs
(a)Null Graph With
Three Vertices.
a b
c
(b)Complete Graph
With Three Vertices.
a b
cc db
a
(c)2-Regular Graph
With Four Vertices.
a
b c
ed
(d)Bipartite Graph With
Five Vertices.
a
b
c
d
d
e
(e)k(3,3) Complete Bipartite
Graph With Six Vertices.
8. Representation Of Graph
Two most common ways to represent a Graph:
1. Adjacency Matrix
2. Adjacency List
Adjacency Matrix:
Adjacency Matrix is a 2D array of size V x V where V is the number of
vertices in a graph.
Let the 2D array be adj [][], a slot adj [i][j] = 1 indicates that there is
an edge from vertex i to vertex j.
Adjacency matrix for undirected graph is always symmetric.
Adjacency Matrix is also used to represent weighted graphs.
If adj [i][j] = w, then there is an edge from vertex i to vertex j with
weight w.
9. Representation Of Graph
Adjacency List:
An array of lists is used.
Size of the array is equal to the number of vertices.
Let the array be array []. An entry array [i] represents the
list of vertices adjacent to the ith vertex.
This representation can also be used to represent a
weighted graph.
The weights of edges can be represented as lists of pairs.
10. Representation Of Graph
Example Of Adjacency Matrix Of A Graph:
a 1 2 3
1 0 1 1
2 1 0 1
b c 3 1 1 0
(a) Matrix Representation Of (a)
Example Of Adjacency List Of A Graph:
a
b c
(a)
Head Node Vertex Node
1 2 3 NULL
2 1 3 NULL
3 1 2 NULL
11. Graph Algorithms
Some Basic Graph Algorithms Are:
1.Depth First Search(DFS)
2.Breadth First Search(BFS)
3.Shortest Path Algorithm
4.Dijskstra’s Algorithm
12. Graph Coloring
Graph Coloring is a method to assign colors to the vertices of a graph
so that no two adjacent vertices have the same color.
Some Graph Coloring problems are :
Vertex coloring : A way of coloring the vertices of a graph so that no
two adjacent vertices share the same color.
Edge Coloring : It is the method of assigning a color to each edge so
that no two adjacent edges have the same color.
Face coloring : It assigns a color to each face or region of a planar
graph so that no two faces that share a common boundary have the
same color.
Chromatic Number:
Chromatic Number is the minimum number of colors required to
color a graph.