Girth

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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.

See also

Cage Graph, Graph Circumference, Graph Cycle, Graph Diameter, Graph Eccentricity, Graph Radius, Moore Graph

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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.

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Girth

Cite this as:

Weisstein, Eric W. "Girth." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/Girth.html

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