To determine To find: The list for the given tree with the help of Prufer’s algorithm. Explanation Algorithm used: Prufer’s algorithm Step 1 (Initialization) (a) Set T to be the given tree. (b) Set k = 1 Step 2 (Choose a k ) While T has more than two vertices Step 2.1 (find a vertex of degree 1) Select from T the vertex X of degree 1 that has the smallest label. Step 2.2 (make a new tree) (a) Find the edge e on X , and let W denote the above vertex on e . (b) Set a k to be the label on W . (c) Delete the edge e and vertex X from T to form a new tree T ′ . Step 2.3 (change T and k ) (a) Replace T with T ′ . (b) Replace k with k + 1 . End while Description: Consider the first graph as shown below. Begin with identifying the vertex with degree 1. Note that the vertex 2 is the vertex of degree 1 which is adjacent to the vertex 1. Thus, label the vertex 1 as a 1 = 1 and delete the edge ( 1 , 2 ) . Let the new graph be T 1 . Further, the vertex 1 is the vertex with degree 1 and it is adjacent to the vertex 5. Thus, label the vertex 5 as a 2 = 5 and delete the edge ( 1 , 5 ) . Now let the new graph be T 2 . Note that the vertex with degree 1 is 3 which is adjacent to the vertex 6

5th Edition

ISBN: 9780134689562

Author: Dossey, John A.

Publisher: Pearson,

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Chapter 5.1, Problem 32E

To determine

To find: The list for the given tree with the help of Prufer’s algorithm.

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Chapter 5.1, Problem 31E

Chapter 5.1, Problem 33E

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Chapter 5 Solutions

Discrete Mathematics

Ch. 5.1 - Prob. 1E Ch. 5.1 - Prob. 2E Ch. 5.1 - Prob. 3E Ch. 5.1 - Prob. 4E Ch. 5.1 - Prob. 5E Ch. 5.1 - Prob. 6E Ch. 5.1 - Prob. 7E Ch. 5.1 - Prob. 8E Ch. 5.1 - Prob. 9E Ch. 5.1 - Prob. 10E

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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