3. We will discuss 3 types of graphs
>BASIC TERMINOLOGIES
>REPRESENTATION OF GRAPH
>OPERATIONS ON GRAPH
4. BASIC TERMINOLOGIES
A directed graph G is defined as an ordered pair (V, E) where, V is a set of vertices and the ordered pairs in E are called edges on V. A directed graph can be represented geometrically as a set of marked points (called vertices) V with a set of arrows (called edges) E between pairs of points (or vertex or nodes) so that there is at most one arrow from one vertex to another vertex.
5. BASIC
TERMINOLOGIES
For example, Figure shows a directed graph, where G = {a, b, c, d }, {(a, b),
(a, d), (d, b), (d, d), (c, c)}
6. which shows the distance in km between four metropolitan cities in India. Here V = {N, K, M, C,} E = {(N, K), (N,M,), (M,K), (M,C), (K,C)} We
= {55,47, 39, 27, 113} and Wv = {N, K, M, C} The weight at the vertices is not necessary to maintain have become the set Wv and V are same.
An undirected graph is said to be connected if there exist a path from any vertex to any other vertex. Otherwise it is said to be disconnected
7.shows the disconnected graph, where the vertex c is not connected to the graph
8.The graph is a mathematical structure and finds its application in many areas, where the problem is to be solved by computers. The problems related to graph G must be represented in computer memory using any suitable data structure to solve the same. There are two standard ways of maintaining a graph G in the memory of a computer.
9.Sequential representation of a graph using adjacent
Linked representation of a graph using linked list
10.In this representation (also called
adjacency list representation), we store
a graph as a linked structure. First we
store all the vertices of the graph in a list
and then each adjacent vertices will be
represented using linked list node. Here terminal vertex of an edge is stored in a structure node and linked to a corresponding initial vertex in the list
11.The weighted graph can be represented using a linked list by storing the corresponding weight along with the terminal vertex of the edge. Consider a weighted graph in Figure, it can be represented using a linked list as in Figure
12. Input the total number of vertices in the graph, say n
Allocate the memory dynamically for the vertices to store in list array
Input the first vertex and the vertices through which it has edge(s) by linking the node from list array through nodes.
Repeat the process by incrementing the list array to add other vertices and edges.
Exit.
13.Input an edge to be searched
Search for an initial vertex of edge in list arrays by incrementing the array
index.
Once it is found, search through the link list for the terminal vertex of the edge.
If found display “the edge is present in the graph”.
Then delete the node where the terminal vertex is found and rearrange the link list.
Exit
3. We will discuss 3 types of graphs
>BASIC TERMINOLOGIES
>REPRESENTATION OF GRAPH
>OPERATIONS ON GRAPH
4. BASIC TERMINOLOGIES
A directed graph G is defined as an ordered pair (V, E) where, V is a set of vertices and the ordered pairs in E are called edges on V. A directed graph can be represented geometrically as a set of marked points (called vertices) V with a set of arrows (called edges) E between pairs of points (or vertex or nodes) so that there is at most one arrow from one vertex to another vertex.
5. BASIC
TERMINOLOGIES
For example, Figure shows a directed graph, where G = {a, b, c, d }, {(a, b),
(a, d), (d, b), (d, d), (c, c)}
6. which shows the distance in km between four metropolitan cities in India. Here V = {N, K, M, C,} E = {(N, K), (N,M,), (M,K), (M,C), (K,C)} We
= {55,47, 39, 27, 113} and Wv = {N, K, M, C} The weight at the vertices is not necessary to maintain have become the set Wv and V are same.
An undirected graph is said to be connected if there exist a path from any vertex to any other vertex. Otherwise it is said to be disconnected
7.shows the disconnected graph, where the vertex c is not connected to the graph
8.The graph is a mathematical structure and finds its application in many areas, where the problem is to be solved by computers. The problems related to graph G must be represented in computer memory using any suitable data structure to solve the same. There are two standard ways of maintaining a graph G in the memory of a computer.
9.Sequential representation of a graph using adjacent
Linked representation of a graph using linked list
10.In this representation (also called
adjacency list representation), we store
a graph as a linked structure. First we
store all the vertices of the graph in a list
and then each adjacent vertices will be
represented using linked list node. Here terminal vertex of an edge is stored in a structure node and linked to a corresponding initial vertex in the list
11.The weighted graph can be represented using a linked list by storing the corresponding weight along with the terminal vertex of the edge. Consider a weighted graph in Figure, it can be represented using a linked list as in Figure
12. Input the total number of vertices in the graph, say n
Allocate the memory dynamically for the vertices to store in list array
Input the first vertex and the vertices through which it has edge(s) by linking the node from list array through nodes.
Repeat the process by incrementing the list array to add other vertices and edges.
Exit.
13.Input an edge to be searched
Search for an initial vertex of edge in list arrays by incrementing the array
index.
Once it is found, search through the link list for the terminal vertex of the edge.
If found display “the edge is present in the graph”.
Then delete the node where the terminal vertex is found and rearrange the link list.
Exit
This slidecast is a tutorial on how to graph linear absolute value functions written in standard form by finding the coordinates of the vertex and using the slope to plot additional points.
This handout is great for teaching GED 2014 math. This handout is not my creation but more my adaptation of information found in several popular resources. The PowerPoint slide picture is from the internet. If I run across again, I would like to give due credit.
Planar graph( Algorithm and Application )Abdullah Moin
A graph is said to be planar if it can be drawn in a plane so that no edge cross. Example: The graph shown in fig is a planar graph. Region of a Graph: Consider a planar graph G=(V, E). A region is defined to be an area of the plane that is bounded by edges and cannot be further subdivided.
Greedy Edge Colouring for Lower Bound of an Achromatic Index of Simple Graphsinventionjournals
International Journal of Engineering and Science Invention (IJESI) is an international journal intended for professionals and researchers in all fields of computer science and electronics. IJESI publishes research articles and reviews within the whole field Engineering Science and Technology, new teaching methods, assessment, validation and the impact of new technologies and it will continue to provide information on the latest trends and developments in this ever-expanding subject. The publications of papers are selected through double peer reviewed to ensure originality, relevance, and readability. The articles published in our journal can be accessed online.
Attributed Graph Matching of Planar GraphsRaül Arlàndez
Many fields such as computer vision, scene analysis, chemistry and molecular biology have
applications in which images have to be processed and some regions have to be searched for
and identified. When this processing is to be performed by a computer automatically without
the assistance of a human expert, a useful way of representing the knowledge is by using
attributed graphs. Attributed graphs have been proved as an effective way of representing
objects. When using graphs to represent objects or images, vertices usually represent regions
(or features) of the object or images, and edges between them represent the relations
between regions. Nonetheless planar graphs are graphs which can be drawn in the plane
without intersecting any edge between them. Most applications use planar graphs to
represent an image.
Graph matching (with attributes or not) represents an NP-complete problem, nevertheless
when we use planar graphs without attributes we can solve this problem in polynomial time
[1]. No algorithms have been presented that solve the attributed graph-matching problem and
use the planar-graphs properties. In this master thesis, we research about Attributed-Planar-
Graph matching. The aim is to find a fast algorithm through studying in depth the properties
and restrictions imposed by planar graphs.
Find the midpoint of two given points.
Find the coordinates of an endpoint given one endpoint and a midpoint.
Find the coordinates of a point a fractional distance from one end of a segment.
This slidecast is a tutorial on how to graph linear absolute value functions written in standard form by finding the coordinates of the vertex and using the slope to plot additional points.
This handout is great for teaching GED 2014 math. This handout is not my creation but more my adaptation of information found in several popular resources. The PowerPoint slide picture is from the internet. If I run across again, I would like to give due credit.
Planar graph( Algorithm and Application )Abdullah Moin
A graph is said to be planar if it can be drawn in a plane so that no edge cross. Example: The graph shown in fig is a planar graph. Region of a Graph: Consider a planar graph G=(V, E). A region is defined to be an area of the plane that is bounded by edges and cannot be further subdivided.
Greedy Edge Colouring for Lower Bound of an Achromatic Index of Simple Graphsinventionjournals
International Journal of Engineering and Science Invention (IJESI) is an international journal intended for professionals and researchers in all fields of computer science and electronics. IJESI publishes research articles and reviews within the whole field Engineering Science and Technology, new teaching methods, assessment, validation and the impact of new technologies and it will continue to provide information on the latest trends and developments in this ever-expanding subject. The publications of papers are selected through double peer reviewed to ensure originality, relevance, and readability. The articles published in our journal can be accessed online.
Attributed Graph Matching of Planar GraphsRaül Arlàndez
Many fields such as computer vision, scene analysis, chemistry and molecular biology have
applications in which images have to be processed and some regions have to be searched for
and identified. When this processing is to be performed by a computer automatically without
the assistance of a human expert, a useful way of representing the knowledge is by using
attributed graphs. Attributed graphs have been proved as an effective way of representing
objects. When using graphs to represent objects or images, vertices usually represent regions
(or features) of the object or images, and edges between them represent the relations
between regions. Nonetheless planar graphs are graphs which can be drawn in the plane
without intersecting any edge between them. Most applications use planar graphs to
represent an image.
Graph matching (with attributes or not) represents an NP-complete problem, nevertheless
when we use planar graphs without attributes we can solve this problem in polynomial time
[1]. No algorithms have been presented that solve the attributed graph-matching problem and
use the planar-graphs properties. In this master thesis, we research about Attributed-Planar-
Graph matching. The aim is to find a fast algorithm through studying in depth the properties
and restrictions imposed by planar graphs.
Find the midpoint of two given points.
Find the coordinates of an endpoint given one endpoint and a midpoint.
Find the coordinates of a point a fractional distance from one end of a segment.
COPD, or chronic obstructive pulmonary (PULL-mun-ary) disease, is a progressive disease that makes it hard to breathe.Chronic obstructive pulmonary disease (COPD), also known as chronic obstructive lung disease (COLD), and chronic obstructive airway disease (COAD).It provides advice and information about COPD, including what the symptoms are, how it can be treated and what steps you can take to manage your condition.
Research Study College Admission Student Digital Media Habits During Post Hig...EnVeritasGroup
This study was conducted to determine how students utilize digital media, including websites, & social media when researching colleges and universities to apply to for admission. It provides marketers insight into the media habits of college students, and is especially beneficial for content marketing agencies and marketing personnel within the
The study provides interesting insights for marketers related to how students shop for schools, what people and other factors influence them, what types of devices they use, and more.