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Given a graph G = (V,E) its complement G is defined to be (V,E) where E = V{2} \ E. That is: a graph on the same vertex-set as G where two vertices are joined in G if and only if they are not joined in G. Prove that if two graphs G₁ & G2 are isomorphic, then their complements G₁ & G2 are isomorphic.

Given a graph G = (V,E) its complement G is defined to be (V,E) where E = V{2} \ E. That is: a graph on the same vertex-set as G where two vertices are joined in G if and only if they are not joined in G. Prove that if two graphs G₁ & G2 are isomorphic, then their complements G₁ & G2 are isomorphic.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Given a graph G = (V,E) its complement G is defined to be (V,E) where E = V{2} \ E. That is: a graph on the same vertex-set as G where two vertices are joined in G if and only if they are not joined in G. Prove that if two graphs G₁ & G2 are isomorphic, then their complements G₁ & G2 are isomorphic.
Transcribed Image Text:Given a graph G = (V,E) its complement G is defined to be (V,E) where E = V{2} \ E. That is: a graph on the same vertex-set as G where two vertices are joined in G if and only if they are not joined in G. Prove that if two graphs G₁ & G2 are isomorphic, then their complements G₁ & G2 are isomorphic.
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