# Chapter 14 - Graph Theory - 14.4 Trees - Exercise Set 14.4: 15

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 5 vertices and 4 edges. Therefore, this graph could be a tree but we can not be sure. It depends how these 4 edges are placed in the graph. It is possible that the edges could be placed in the graph such that a circuit is created and that the graph is not connected.

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