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= (5) 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.

= (5) 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.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.5: Graphs Of Functions
Problem 48E
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= (5) 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:= (5) 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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