   Chapter 10.3, Problem 22ES ### 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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# Prove that each of the properties in 21-29 is an invariant for graph isomorphism. Assume that n, m, and k are all nonnegative integers.Has m edges

To determine

To prove:

Prove that the property (has m edges) is an invariant for graph isomorphism.

Explanation

Given information:

Assume that n, m and k are all nonnegative integers.

Proof:

Let G and G be isomorphic graphs and let the graph G contain m edges.

We then need to show that G has m edges as well.

Let E ( G ) be the set of edges of G and let E(G) be the set of edges of G.

Since G and G’ are isomorphic, there exists a one-to-one correspondence h between E ( G ) and E(G). However, a one-to-one correspondence only exists between two sets that have the same number of elements

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