## Thinking Mathematically (6th Edition)

One characteristic of a tree is the following: If the tree has $n$ vertices, then the tree has $n-1$ edges. The original graph in this exercise has 9 vertices so the spanning tree must include all 9 vertices and we need to include 8 edges in the spanning tree. To make a spanning tree from the original graph, we can use the edges FC, CB, BA, AE, ED, DG, GH, and HI. The spanning tree has 9 vertices and 8 edges and every edge is a bridge. The spanning tree is connected and there are no circuits. Therefore, this is a valid spanning tree. This is one spanning tree, but other spanning trees are possible.