Java presentation final
Transcript of 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!