Explanation Algorithm used: Depth First Search Algorithm. Step 1 (label the starting vertex) Select a vertex U , assign U the label L , and let U have no predecessor. Set L = { U } and T = ϕ . Set k = 2 and X = U . Step 2 (label other vertices) Repeat Step 2.1 (label a vertex adjacent to X ) While there is a vertex Y not in L that is adjacent to X . ( Place the edge { X , Y } in T Assign X to be the predecessor of Y . Assign Y the label k . Include Y in C . Replace k with k + 1 . Now let X denote the vertex Y . End while Step 2.2 (back up) Replace X with the predecessor of X . Until X = null or every vertex of G is in L Step 3 (is there a spanning tree?) If every vertex of G is in L . The edges in T and their incident vertices form a spanning tree of Q Otherwise There is no spanning tree for G because Q is not connected

5th Edition

ISBN: 9780134689562

Author: Dossey, John A.

Publisher: Pearson,

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Question

Chapter 5.3, Problem 9E

To determine

To plot: The spanning tree of the given graph with the help of theorem 5.7 and first-depth-search algorithm.

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Chapter 5.3, Problem 8E

Chapter 5.3, Problem 10E

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Chapter 5 Solutions

Discrete Mathematics

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