Girth
المؤلف:
Harary, F.
المصدر:
Graph Theory. Reading, MA: Addison-Wesley
الجزء والصفحة:
...
28-2-2022
2037
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.
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