Discrete Mathematics and Its Applications, Seventh Edition

Published by McGraw-Hill Education
ISBN 10: 0073383090
ISBN 13: 978-0-07338-309-5

Chapter 11 - Section 11.4 - Spanning Trees - Exercises - Page 796: 19

Answer

Describing the trees produced by breadth-first search and depth-first search of the wheel graph Wn, starting at the vertex of degree n, where n is an integer with n ≥ 3.

Work Step by Step

--With breadth-first search, - the initial vertex is the middle vertex, and the n spokes are added to the tree as this vertex is processed. Thus, - the resulting tree is K1,n. With depth-first search, we start at the vertex in the middle of the wheel and visit a neighbor—one of the vertices on the rim. -From there we move to an adjacent vertex on the rim, - and so on all the way around until we have reached every vertex. Thus, -- the resulting spanning tree is a path of length n.
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