close
Image TOPICS
Image
Search

Zero-Symmetric Graph

DOWNLOAD Mathematica NotebookDownload Wolfram Notebook
ZeroSymmetricGraphs

A zero-symmetric graph is a vertex-transitive cubic graph whose edges are partitioned into three orbits by its automorphism group. The figures above show some small zero-symmetric graphs.

Image

An embedding of the smallest zero-symmetric graph appears on the cover of Coxeter et al. (1981) and on p. 5.

See also

Cubic Vertex-Transitive Graph, Great Rhombicosidodecahedral Graph, Great Rhombicuboctahedral Graph, Haar Graph

Portions of this entry contributed by Simone Severini

Explore with Wolfram|Alpha

References

Coxeter, H. S. M.; Frucht, R.; and Powers, D. L. Zero-Symmetric Graphs: Trivalent Graphical Regular Representations of Groups. New York: Academic Press, 1981.Hladnik, M.; Marušič, D.; and Pisanski, T. "Cyclic Haar Graphs." Disc. Math. 244, 137-153, 2002.

Referenced on Wolfram|Alpha

Zero-Symmetric Graph

Cite this as:

Severini, Simone and Weisstein, Eric W. "Zero-Symmetric Graph." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/Zero-SymmetricGraph.html

Subject classifications