Java presentation final

GRAPHS

Created By Wesley Wilson Shrayas Suryakumar Tahir Hussain Querashi

IntroductionBasically we use word graph for the mention any roadmap,Network design , root design , network design ,etc.

Graphs uses for simulating electrical circuits which finds outs the current and voltage passes through various electrical components presents in the circuit, telephone network connection , internet connection

Defination of Graph :-

Graph Theory

A graph contains pair of finite set of vertex and edges.

Where V=Set of vertices/nodes E=Set of edges/arcs

Size of graph :-

Number of elements in the vertex set is called as size of graph.

Sub-Graph :-

Let G={V,E} and G’={V’,E’} , If V’ᴄ V and E’ᴄ E then G’ is called as Sub-Graph of G’

Spanning Sub-Graph :-

Let G={V,E} and G’={V’,E’} , If V’= V and then G’ is called as Sub-Graph of G’.

Completed Graph :-

Completed Graph is a simple graph in which every vertex connected by edge to the remaining vertices. If there are n vertices then there are total edges in completed graph.

Degree of vertex :-

The number of edges that are incident upon the vertex is called as degree

Spanning Tree :-

A graph is connected acyclic spanning subgraph.

Diagraph :-

If each edge is represented by a pair of ordered vertices that is edge has specific direction.

Indegree of vertex :-

Total no. of incoming edges for vertex in the diagraph.

Outdegree of vertex :-

Total no. Of outgoing edges for vertex in the diagraph.

Weighted diagraph :-

A weight may be associated with each edge of a graph.

Graph Representation

1. Adjacency Matrix :-

An Adjacency matrix for the graph is the two dimensional Boolean array.

Incident Matrix :-

An incident matrix for the graph is the two-dimensional integer array.

Adjacency List :-

A list contains one element for each vertex in the graph and in which each vertex list element contains a list of the vertices that are adjacent to its vertex, such list is called Adjacency List.Edge List is a secondary List for each vertex.

Thank You!