   Chapter 10.4, Problem 6ES ### 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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# If graphs are allowed to have an infinite number of vertices and edges. then Lemma 10.4.1 is false. Give a counterexample that shows this. In other words. give an example of an “infinite tree” (a connected. circuit-free graph with an infinite number of vertices and edges) that has no vertex of degree 1.

To determine

To find:

An example of an infinite tree, which has no vertex of degree 1.

Explanation

Given information:

Lemma

Concept used:

Any tree that has more than one vertex has at least one vertex of degree 1.

Graph:

Assume a graph with n vertices v0,v1,v2,v3,v4,.......,vn.

Consider the following definitions:

1. Connected graph: A graph is said to be connected graph if and only if, for any two given vertices in the graph, there exists a walk between those two vertices

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