   Chapter 10.1, Problem 53ES ### 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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# For what values of n dies the complete graph Kn with n vertices have (a) an Euler circuit? (b) a Hamiltonian circuit? Justify your answers.

To determine

(a)

For what values of n does the complete graph Kn with n vertices have an Euler circuit?

Explanation

Given information:

an Euler circuit.

Calculation:

Kn is a simple graph with n vertices v1,v2,...,vn and an edge between every pair of vertices.

An Euler circuit exists when the graph is connected and when every vertex of the graph has an even degree.

Kn is a connected graph, because there is an edge between every pair of vertices. Since each vertex is connected to the other n − 1 vertices by an edge, the degree of every vertex vi is n − 1

To determine

(b)

For what values of n does the complete graph Kn with n vertices have a Hamiltonian circuit?

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