Explanation Description: It is given that the total number of vertices in a rooted tree with p interval vertices and each of the vertices have q children are p q + 1 . This can be proved by the principal of mathematical induction as follows. Consider that p = 1 . Then the root is only an internal vertex and it has q children. Therefore, the total number of vertices is obtained as follows. q + 1 = 1 ⋅ q + 1 = p q + 1 Now, consider that the given statement is true for p = k . That is, when the number of internal vertices are k and each of the vertices have q children, then the net number of vertices in the rooted tree is k q + 1 . Now prove the statement for p = k + 1

5th Edition

ISBN: 9780134689562

Author: Dossey, John A.

Publisher: Pearson,

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Question

Chapter 5, Problem 28SE

To determine

The number of terminal vertices in a rooted tree with p internal vertices and each vertex has q children.

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Chapter 5, Problem 27SE

Chapter 5, Problem 29SE

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Chapter 5 Solutions

Discrete Mathematics

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Ch. 5.1 - Seven farming communities in Iowa want to develop...Ch. 5.1 - As few trails as possible are to be built between...Ch. 5.1 - A farmer needs to irrigate the fields in which his...Ch. 5.1 - Draw a graph that is not a tree for which the...Ch. 5.1 - Prob. 15E Ch. 5.1 - What is the smallest number of edges in a...Ch. 5.1 - Prob. 17E Ch. 5.1 - Prob. 18E Ch. 5.1 - Prob. 19E Ch. 5.1 - Prob. 20E Ch. 5.1 - Prob. 21E Ch. 5.1 - Prob. 22E Ch. 5.1 - There are two saturated hydrocarbons of the type...Ch. 5.1 - Prob. 24E Ch. 5.1 - Prob. 25E Ch. 5.1 - Prob. 26E Ch. 5.1 - Prob. 27E Ch. 5.1 - Prob. 28E Ch. 5.1 - In order to count the number of distinct trees...Ch. 5.1 - Prob. 30E Ch. 5.1 - Prob. 31E Ch. 5.1 - In order to count the number of distinct trees...Ch. 5.1 - Prob. 33E Ch. 5.1 - Prob. 34E Ch. 5.1 - Prob. 35E Ch. 5.1 - Prob. 36E Ch. 5.1 - Prob. 37E Ch. 5.1 - Prob. 38E Ch. 5.1 - Prob. 39E Ch. 5.1 - Prob. 40E Ch. 5.1 - Prob. 41E Ch. 5.1 - Prob. 42E Ch. 5.1 - Prob. 43E Ch. 5.1 - Prob. 44E Ch. 5.1 - 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