   Chapter 10.3, Problem 7ES ### Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
ISBN: 9781337694193

#### Solutions

Chapter
Section ### Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
ISBN: 9781337694193
Textbook Problem
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# For each pair of graphs G and G’ in 6-13, determine whether G and G’ are isomorphic. If they are, give functions g: V(G) → V(G’) and h:E(G) → E(G’) that define the isomorphism. If they are not, give an invariant for graph isomorphism that they do not share. To determine

Whether G and G are isomorphic. If they are, give functions g:V(G)V(G) and h:E(G)E(G) that define the isomorphism. If they are not, give an invariant for graph isomorphism that they do not share.

Explanation

Given information:

Calculation:

Two graphs are G and G (with vertices V ( G ) and V(G) respectively and edges E ( G ) and E(G) respectively) are isomorphic if there exists one-to-one correspondence such that

[u,v] is an edge in G[g(u),g(v)] is an edge of G.

V(G) are all vertices of the graph GV(G')are all vertices of the graph G'

V(G)={v1,v2,v3,v4}V(G)={w1,w2,w3,w4}

Let us define the function g:V(G)V(G) as in the arrow diagrams below.

We note that both functions are one-to-one correspondence, because no elements are the image of more than one element and both sets have the same number of elements.

[u,v] is an edge in G            [g(u),g(v)] is an edge of G

[v1,v2

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