Explanation It is known that depth first search algorithm is used to find the spanning tree in a connected graph. Label the vertices with consecutive integers that indicate the sequence in which the vertices are encountered. It is to find the vertex that should be labeled immediately after labeling vertex v , the first vertices to consider are the unlabeled with the one adjacent to v . If there is an unlabeled vertex w adjacent to v , then w is assigned the next label number and the process of searching for the next vertex to label is begun with w . If v has no unlabeled adjacent vertices, back up along the edge that was traversed to label v and continue backing up, if necessary. That means the search continues at v − 1 vertex if it has other vertices adjacent. Otherwise, the backing up goes to v − 2 and so on. In the depth first search algorithm, L is the set of vertices with labels, the predecessors of the vertex Y is a vertex in L that is used in labeling Y , and T is the set of edges that join each vertex to its predecessor

5th Edition

ISBN: 9780134689562

Author: Dossey, John A.

Publisher: Pearson,

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Chapter 5, Problem 32SE

To determine

To prove: That when depth first search algorithm is applied to a connected graph, one of the vertices on an edge is an ancestor of the other.

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Chapter 5, Problem 31SE

Chapter 5, Problem 33SE

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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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