Explanation Algorithm used: Kruskal’s Algorithm. Step 1 (initialization) Set T = ϕ . Let S be the set of all edges of G . Step 2 (enlarge T ) While | T | < n − 1 and S is not empty Choose an edge e of smallest weight from S . (Ties can be broken arbitrarily.) If no cycle is formed by any of the edges in T ∪ { e } , then replace T with T ∪ { e } . Remove e from S . Endwhile Step 3 (is there a minimal spanning tree?) If | T | < n − 1 There is no minimal spanning tree for G because it is not connected Otherwise The edges in T and their incident vertices form a minimal spanning tree. Endif Description: Consider the following graph. Begins with defining the sets. Set T = ϕ and S = { a , b , c , d , e , f , g , h , i , j , k , m , n , o , p , q , r , s , t , u , v , w } . In set S, the edge k is the edge which has the smallest weight so add k into T and delete it from S

5th Edition

ISBN: 9780134689562

Author: Dossey, John A.

Publisher: Pearson,

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Chapter 5.2, Problem 41E

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To graph: A minimal spanning tree for the given weighted graph with the help of minimal spanning tree.

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Chapter 5.2, Problem 40E

Chapter 5.2, Problem 42E

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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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