Thinking Mathematically (6th Edition)

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

Chapter 14 - Graph Theory - 14.4 Trees - Exercise Set 14.4: 16

Answer

iii. The described graph may or may not be a tree.

Work Step by Step

iii. The described graph may or may not be a tree. A tree is a graph that is connected and has no circuits. A graph is connected when there is a path between every pair of vertices. One characteristic of a tree is the following: If the graph has $n$ vertices, then the graph has $n-1$ edges. This graph has 4 vertices and 3 edges. Therefore, this graph could be a tree but we can not be sure. It depends how these 3 edges are placed in the graph. It is possible that the 3 edges could be placed in the graph such that a circuit is created among 3 vertices and that the other vertex is not connected to any of the other 3 vertices.
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