Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
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.

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter3: Matrices
Section3.7: Applications
Problem 80EQ
See similar textbooks
icon
Related questions
Question
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.
Expert Solution
steps

Step by step

Solved in 3 steps with 3 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
SEE MORE TEXTBOOKS