## Thinking Mathematically (6th Edition)

One characteristic of a tree is the following: If the graph has $n$ vertices, then the graph has $n-1$ edges. The original graph has 6 vertices and 6 edges. Therefore this graph is not a tree. However, by removing any one of the 6 edges, the graph will have 6 vertices and 5 edges. Also, the graph will still be connected and there will be no circuit. Therefore, the graph will be a tree. For example, to make a spanning tree, we could remove the edge AB.