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Locally Petersen Graph

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A locally Petersen graph is a graph Gamma for which the induced subgraph on the vertices adjacent to each graph vertex t (i.e., the neighborhood graph) is isomorphic to the Petersen graph. There are exactly three graph isomorphism classes of connected locally Petersen graphs, as summarized in the following table (Hall 1980).

nsymbolgraphintersection array
21Gamma^((1))(7,2)-Kneser graph{10,6;1,6}
63Gamma^((2))Conway-Smith graph{10,6,4,1;1,2,6,10}
65Gamma^((3))Hall graph{10,6,4;1,2,5}

See also

Conway-Smith Graph, Hall Graph, Kneser Graph, Local Graph, Petersen Graph

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References

Brouwer, A. E.; Cohen, A. M.; and Neumaier, A. §1.16.5 in Distance Regular Graphs. New York: Springer-Verlag, p. 37, 1989.Hall, J. I. "Locally Petersen Graphs." J. Graph Th. 4, 173-187, 1980. https://doi.org/10.1002/jgt.3190040206.House of Graphs. Locally Petersen Graphs. Kneser K(7,2), Conway Smith Graph, and Hall Graph.

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Locally Petersen Graph

Cite this as:

Weisstein, Eric W. "Locally Petersen Graph." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/LocallyPetersenGraph.html

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