Quartic Vertex-Transitive Graph


A quartic vertex-transitive graph is a quartic graph that is vertex transitive. Read and Wilson (1988, pp. 164-166) enumerate all connected quartic vertex-transitive graphs on 19 and fewer nodes, some of which are illustrated above.

The quartic symmetric graphs are a special case of the quartic vertex-transitive graphs (i.e., those that are also edge-transitive).

Classes of connected quartic vertex-transitive graphs include the antiprism graphs. Specific cases are summarized in the following table. In particular, Qt31 can be constructed as the distance-3 graph of the Heawood graph or as the Levi graph of the biplane on 7 points ( It is also a distance-regular graph with intersection array {4,3,2;1,2,4} that is also distance-transitive.

See also

Cubic Vertex-Transitive Graph, Quartic Graph, Quartic Symmetric Graph, Vertex-Transitive Graph

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References "Distance-3 Graph of Heawood Graph = Incidence Graph of Biplane on 7 Points.", R. C. and Wilson, R. J. An Atlas of Graphs. Oxford, England: Oxford University Press, pp. 164-166, 1998.

Referenced on Wolfram|Alpha

Quartic Vertex-Transitive Graph

Cite this as:

Weisstein, Eric W. "Quartic Vertex-Transitive Graph." From MathWorld--A Wolfram Web Resource.

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