   Chapter 10.4, Problem 3ES ### 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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# What is the total degree of a tree with n vertices? Why?

To determine

To find:

The total degree of tree with n vertices and give reason also.

Explanation

Given information:

The total degree of a tree with vertices.

Concept used:

First prove that the number of edges in graph G is equal to n1, using induction method. Here n is the number of vertices.

This is true for n=1,2,3.

Calculation:

Let G be a tree with n vertices and e be an edge with end vertices u and v.

That means that the path between u and v is e.

Therefore, deletion of e from G disconnects G.

Assume that Ge consists of exactly two components namely G1 and G2.

There were no cycles to begin with, hence each component is a tree.

The tree is shown below.

Take n1 and n2 as the number of vertices in G1 and G2 respectively.

Thus, n1+n2=n and n1<n,n2<n

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