   Chapter 10.4, Problem 6TY ### 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 any positive integer n, any tree with n vertices has ______.

To determine

To fill:

For any positive integer n, any tree with n vertices has _____.

Explanation

Given information:

The incomplete statement “For any positive integer n, any tree with n vertices has _____.”

For any positive integer n, any tree with n vertices has n - 1 edges

Let it be true for a positive integer k and then show it is true for k + 1.

Thus assume, that a tree T with k + 1 vertices, and must show that T has (k+1)1=k

edges.

By Lemma 10.4.1, T has a vertex v of degree 1, and since T is connected, v is attached to the rest of T by a single edge e.

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