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Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
ISBN: 9781337694193

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BuyFindarrow_forward

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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Sect-10.1 P-2ESSect-10.1 P-3ESSect-10.1 P-4ESSect-10.1 P-5ESSect-10.1 P-6ESSect-10.1 P-7ESSect-10.1 P-8ESSect-10.1 P-9ESSect-10.1 P-10ESSect-10.1 P-11ESSect-10.1 P-12ESSect-10.1 P-13ESSect-10.1 P-14ESSect-10.1 P-15ESSect-10.1 P-16ESSect-10.1 P-17ESSect-10.1 P-18ESSect-10.1 P-19ESSect-10.1 P-20ESSect-10.1 P-21ESSect-10.1 P-22ESSect-10.1 P-23ESSect-10.1 P-24ESSect-10.1 P-25ESSect-10.1 P-26ESSect-10.1 P-27ESSect-10.1 P-28ESSect-10.1 P-29ESSect-10.1 P-30ESSect-10.1 P-31ESSect-10.1 P-32ESSect-10.1 P-33ESSect-10.1 P-34ESSect-10.1 P-35ESSect-10.1 P-36ESSect-10.1 P-37ESSect-10.1 P-38ESSect-10.1 P-39ESSect-10.1 P-40ESSect-10.1 P-41ESSect-10.1 P-42ESSect-10.1 P-43ESSect-10.1 P-44ESSect-10.1 P-45ESSect-10.1 P-46ESSect-10.1 P-47ESSect-10.1 P-48ESSect-10.1 P-49ESSect-10.1 P-50ESSect-10.1 P-51ESSect-10.1 P-52ESSect-10.1 P-53ESSect-10.1 P-54ESSect-10.1 P-55ESSect-10.1 P-56ESSect-10.1 P-57ESSect-10.2 P-1TYSect-10.2 P-2TYSect-10.2 P-3TYSect-10.2 P-4TYSect-10.2 P-5TYSect-10.2 P-6TYSect-10.2 P-1ESSect-10.2 P-2ESSect-10.2 P-3ESSect-10.2 P-4ESSect-10.2 P-5ESSect-10.2 P-6ESSect-10.2 P-7ESSect-10.2 P-8ESSect-10.2 P-9ESSect-10.2 P-10ESSect-10.2 P-11ESSect-10.2 P-12ESSect-10.2 P-13ESSect-10.2 P-14ESSect-10.2 P-15ESSect-10.2 P-16ESSect-10.2 P-17ESSect-10.2 P-18ESSect-10.2 P-19ESSect-10.2 P-20ESSect-10.2 P-21ESSect-10.2 P-22ESSect-10.2 P-23ESSect-10.3 P-1TYSect-10.3 P-2TYSect-10.3 P-3TYSect-10.3 P-1ESSect-10.3 P-2ESSect-10.3 P-3ESSect-10.3 P-4ESSect-10.3 P-5ESSect-10.3 P-6ESSect-10.3 P-7ESSect-10.3 P-8ESSect-10.3 P-9ESSect-10.3 P-10ESSect-10.3 P-11ESSect-10.3 P-12ESSect-10.3 P-13ESSect-10.3 P-14ESSect-10.3 P-15ESSect-10.3 P-16ESSect-10.3 P-17ESSect-10.3 P-18ESSect-10.3 P-19ESSect-10.3 P-20ESSect-10.3 P-21ESSect-10.3 P-22ESSect-10.3 P-23ESSect-10.3 P-24ESSect-10.3 P-25ESSect-10.3 P-26ESSect-10.3 P-27ESSect-10.3 P-28ESSect-10.3 P-29ESSect-10.3 P-30ESSect-10.4 P-1TYSect-10.4 P-2TYSect-10.4 P-3TYSect-10.4 P-4TYSect-10.4 P-5TYSect-10.4 P-6TYSect-10.4 P-7TYSect-10.4 P-1ESSect-10.4 P-2ESSect-10.4 P-3ESSect-10.4 P-4ESSect-10.4 P-5ESSect-10.4 P-6ESSect-10.4 P-7ESSect-10.4 P-8ESSect-10.4 P-9ESSect-10.4 P-10ESSect-10.4 P-11ESSect-10.4 P-12ESSect-10.4 P-13ESSect-10.4 P-14ESSect-10.4 P-15ESSect-10.4 P-16ESSect-10.4 P-17ESSect-10.4 P-18ESSect-10.4 P-19ESSect-10.4 P-20ESSect-10.4 P-21ESSect-10.4 P-22ESSect-10.4 P-23ESSect-10.4 P-24ESSect-10.4 P-25ESSect-10.4 P-26ESSect-10.4 P-27ESSect-10.4 P-28ESSect-10.4 P-29ESSect-10.4 P-30ESSect-10.4 P-31ESSect-10.5 P-1TYSect-10.5 P-2TYSect-10.5 P-3TYSect-10.5 P-4TYSect-10.5 P-5TYSect-10.5 P-1ESSect-10.5 P-2ESSect-10.5 P-3ESSect-10.5 P-4ESSect-10.5 P-5ESSect-10.5 P-6ESSect-10.5 P-7ESSect-10.5 P-8ESSect-10.5 P-9ESSect-10.5 P-10ESSect-10.5 P-11ESSect-10.5 P-12ESSect-10.5 P-13ESSect-10.5 P-14ESSect-10.5 P-15ESSect-10.5 P-16ESSect-10.5 P-17ESSect-10.5 P-18ESSect-10.5 P-19ESSect-10.5 P-20ESSect-10.5 P-21ESSect-10.5 P-22ESSect-10.5 P-23ESSect-10.5 P-24ESSect-10.5 P-25ESSect-10.6 P-1TYSect-10.6 P-2TYSect-10.6 P-3TYSect-10.6 P-4TYSect-10.6 P-5TYSect-10.6 P-6TYSect-10.6 P-7TYSect-10.6 P-1ESSect-10.6 P-2ESSect-10.6 P-3ESSect-10.6 P-4ESSect-10.6 P-5ESSect-10.6 P-6ESSect-10.6 P-7ESSect-10.6 P-8ESSect-10.6 P-9ESSect-10.6 P-10ESSect-10.6 P-11ESSect-10.6 P-12ESSect-10.6 P-13ESSect-10.6 P-14ESSect-10.6 P-15ESSect-10.6 P-16ESSect-10.6 P-17ESSect-10.6 P-18ESSect-10.6 P-19ESSect-10.6 P-20ESSect-10.6 P-21ESSect-10.6 P-22ESSect-10.6 P-23ESSect-10.6 P-24ESSect-10.6 P-25ESSect-10.6 P-26ESSect-10.6 P-27ESSect-10.6 P-28ESSect-10.6 P-29ESSect-10.6 P-30ESSect-10.6 P-31ES