Girth

The girth of a graphs is the length of one of its (if any) shortest graph cycles. Acyclic graphs are considered to have infinite girth (Skiena 1990, p. 191). The girth of a graph may be found using Girth[g] in the Wolfram Language package Combinatorica` . Precomputed girths for many named graphs can be obtained using GraphData[graph, "Girth"].

The following table gives examples of graphs with various girths.

girth	example
3	tetrahedral graph, complete graph
4	cubical graph, utility graph
5	Petersen graph
6	Heawood graph
7	McGee graph
8	Levi graph

REFERENCES

Harary, F. Graph Theory. Reading, MA: Addison-Wesley, p. 13, 1994.

Skiena, S. "Girth." §5.3.2 in Implementing Discrete Mathematics: Combinatorics and Graph Theory with Mathematica. Reading, MA: Addison-Wesley, pp. 190-192, 1990.