Thinking Mathematically (6th Edition)

Published by Pearson
ISBN 10: 0321867327
ISBN 13: 978-0-32186-732-2

Chapter 14 - Graph Theory - Chapter 14 Test: 11

Answer

(a) We can use a graph to model the connecting relationships in the floor plan. (b) Since the graph has no Euler paths, there is no path that uses each door exactly once. (c) No such path is possible.
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Work Step by Step

(a) We can use a graph to model the connecting relationships in the floor plan. Each vertex represents one room (and vertex G represents the outside) and each edge represents a common door between two rooms. (b) We need to verify the number of odd vertices. Vertex A, vertex C, vertex D, and vertex E are odd vertices. The graph has exactly four odd vertices. Therefore, the graph does not have any Euler paths. Since the graph has no Euler paths, there is no path that uses each door exactly once. (c) No such path is possible.
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