   Chapter 10.1, Problem 27ES ### 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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# Let G be a simple graph with n vertices. What is the relation between the number of edges of G and the number of edges of the complement G’?

To determine

To find:

The relation between the number of edges of G and the number of edges of the complement G’.

Explanation

Given information:

G be a simple graph with n vertices.

Formula used:

The number of edges of a completed graph is n(n1)2 for n vertices.

Definition used:

The complement of a graph G is a graph H on the same vertices such that two distinct vertices of H are adjacent if and only if they are not adjacent in G.

Calculation:

G be a simple graph with n vertices. (Given)

The number of edges of a completed graph is n(n1)2.

Suppose the graph G has k vertices, then the complement graph G’ contains n(n1)2k edges

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