DM_10 - Discrete Mathematics(CSC 1204 9.3 Representing Graphs and Graph Isomorphism 1 Representing Graphs and Graph Isomorphism Graph Representation

DM_10 - Discrete Mathematics(CSC 1204 9.3 Representing...

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Discrete Mathematics (CSC 1204) 9.3 Representing Graphs and Graph Isomorphism 1
Representing Graphs and Graph Isomorphism Graph Representation : Adjacency lists Adjacency matrices Incidence matrices Graph isomorphism: Two graphs are isomorphic iff they are identical except for their node names 2
Representing Graphs One way to represent a graph without multiple edges is to list all the edges of the graph. Another way to represent a graph with no multiple edges is to use adjacency lists , which specify the vertices that are adjacent to each vertex of the graph. Adjacency Lists : A table with 1 row per vertex , listing its adjacent vertices. Directed Adjacency Lists : A table with 1 row per node , listing the terminal nodes of each edge incident from that node . 3
Representing Graphs EXAMPLE 1(p.612): Use adjacencyliststo describe the simple graph given in Figure 1. 4
Representing Graphs EXAMPLE 2(p.612): Represent the directed graph shown in Figure 2 by listing all the vertices that are the terminal vertices of edges starting at each vertex of the graph. 5
Representing Graphs Two types of matrices commonly used to represent graphs – 1) Adjacency matrix 2) Incidence matrix Adjacency matrix : A matrix representing a graph using the adjacency of vertices . Incidence matrix : A matrix representing a graph using the incidence of edges and vertices . 6
Adjacency matrices Suppose that G = (V, E) is a simple graph where |V|= n. Suppose that the vertices of G are listed arbitrarily as v1, v2, …., vn. The adjacency matrix Aof G, with respect to this listing of the vertices, is the n x n zero-one matrix with 1 as its (i,j)th entry when viand vj are adjacent, and 0 as its (i,j)th entry when they are not adjacent.In other words, if its adjacency matrix is A= [ aij], thenaij= 1if {vi, vj} is an edge of G,0otherwise 7
Adjacency matrices : Example 3(p.612) 8

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