group of a graph is a free group, in which the number of generators is exactly the number of edges in . This number equals .

For example, suppose has 16 vertices arranged in 4 rows of 4 vertices each, with edges connecting vertices that are adjacent horizontally or vertically. Then has 24 edges overall, and the number of edges in each spanning tree is 16 - 1 {{= 15}}, so the fundamental group of is the free group with 9 generators. Note that