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. Explanation Description: It is known that depth first search algorithm is utilized 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 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. Also, 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 33SE

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 32SE

Chapter 5, Problem 34SE

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