Explanation Given: A table representing the possibility of a pipe. Bin 1 2 3 4 5 6 7 1 - 4 - 6 2 - 3 2 4 - 5 2 - 3 1 3 - 5 - 7 - 2 2 4 6 2 7 - 4 1 - 5 2 - - 4 - 1 - 6 - 3 2 1 1 - 2 7 3 1 2 - - 2 - Algorithm used: Prim’s algorithm . Step 1 (Select starting vertex) Select vertex U . and set L ( U ) and T = ϕ Step 2 (enlarge T ) While some edge has one vertex in L and one not in L . Choose an edge of smallest weight from among those with one vertex in L and the other not in L . (Ties can be broken arbitrarily.) Place the edge in T Place its vertices in L (one of these is already in L ). Endwhile Step 3 (is there a minimal spanning tree?) If | L | < n The graph is not connected, and so it has no minimal spanning tree. Otherwise The edges in T and their incident vertices from a minimal spanning tree. Spanning tree. A snapping tree of a graph G is a tree formed by containing all the vertices of the original graph G . Description: Let the bins be represented by A , B , C , D , E , F , G . Thus, the table can be modified as below. Bin A B C D E F G A - 4 - 6 2 - 3 B 4 - 5 2 - 3 1 C - 5 - 7 - 2 2 D 6 2 7 - 4 1 - E 2 - - 4 - 1 - F - 3 2 1 1 - 2 G 3 1 2 - - 2 - The meaning ( − ) is that there is no possibility of any pipe that can be built in between the corn bins and the meaning of a value is the cost of the pipe

5th Edition

ISBN: 9780134689562

Author: Dossey, John A.

Publisher: Pearson,

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Chapter 5.2, Problem 29E

To determine

To find: The way that the pipes can be built with a minimal cost.

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Chapter 5.2, Problem 28E

Chapter 5.2, Problem 30E

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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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