Automorphic Graph

An automorphic graph is a distance-transitive graph Gamma for which the automorphism group Aut(Gamma) acts primitively on the vertices of Gamma and is not a complete graph or an line graph (Biggs 1993, p. 178).

The following table summarizes some known automorphic graphs (Gordon and Levingston 1981; Biggs 1976; Biggs 1993, pp. 178-179). There are exactly three cubic automorphic graphs, and a single quartic automorphic graph (Biggs 1976). Note that odd graphs are automorphic (Biggs 1976).

See also

Automorphism Group, Distance-Transitive Graph

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Biggs, N. L. Algebraic Graph Theory, 2nd ed. Cambridge, England: Cambridge University Press, 1993.Biggs, N. L. "Automorphic Graphs and the Krein Condition." Geom. Dedicata 5, 117-127, 1976.Buekenhout, F. and Rowlinson, P. "The Uniqueness of Certain Automorphic Graphs." Geom. Dedicata 11, 443-446, 1981.Gordon, L. M. and Levingston, R. "The Construction of Some Automorphic Graphs." Geom. Dedicata 10, 261-267, 1981.Hall, J. I. "Locally Petersen Graphs." J. Graph Th. 4, 173-187, 1980.

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Automorphic Graph

Cite this as:

Weisstein, Eric W. "Automorphic Graph." From MathWorld--A Wolfram Web Resource.

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