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 (DistanceRegular.org). It is also a distance-regular
graph with intersection array that is also distance-transitive .

See also Cubic Vertex-Transitive Graph ,

Quartic Graph ,

Quartic
Symmetric Graph ,

Vertex-Transitive Graph
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References DistanceRegular.org. "Distance-3 Graph of Heawood Graph
Incidence Graph of Biplane on 7 Points." http://www.distanceregular.org/graphs/heawood-dist3.html . Read,
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. https://mathworld.wolfram.com/QuarticVertex-TransitiveGraph.html

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