In graph theory
, the girth
of a graph is the length of the shortest cycle contained in the graph. If the graph doesn't contain any cycles, its girth is defined to be infinity
For example, a 4-cycle (square) has girth 4. A grid has girth 4 as well, and a triangular mesh has girth 3.
The Heawood graph in the figure on the left is the smallest trivalent graph with girth 6; the Petersen graph on the right is the smallest trivalent graph with girth 5.
In common usage, girth refers to the circumference
of a cylindrical object such as a tree trunk