## Thinking Mathematically (6th Edition)

ii. The described graph is not 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 8 vertices but it has only 5 edges. Therefore, this graph is not a tree.