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
Prove that the property (has m edges) is an invariant for graph isomorphism.
Assume that n, m and k are all nonnegative integers.
Let G and be isomorphic graphs and let the graph G contain m edges.
We then need to show that has m edges as well.
Let E ( G ) be the set of edges of G and let be the set of edges of .
Since G and G’ are isomorphic, there exists a one-to-one correspondence h between E ( G ) and . However, a one-to-one correspondence only exists between two sets that have the same number of elements
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