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Raiskii Graph

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RaiskiiGraph

The Raiskii graph is the 8-vertex, 18-edge graph illustrated above. It has graph diameter 2 and girth 3.

It is the smallest graph with graph dimension 3 and chromatic number 5 (Nechushtan 2002). Its unit-distance embedding in R^3 gives the lower bound chi(R^3)>=5, the n=3 case of Raiskii's general bound chi(R^n)>=n+2 (Raiskii 1970).

The Raiskii graph is implemented in the Wolfram Language as GraphData["RaiskiiGraph"].

See also

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References

House of Graphs. "Raiskii Graph." https://houseofgraphs.org/graphs/45654.Nechushtan, O. "On the Space Chromatic Number." Disc. Math. 256, 499-507, 2002. https://doi.org/10.1016/S0012-365X(00)00406-4.Raiskii, D. E. "The Realization of All Distances in a Decomposition of the Space R^n into n+1 Parts." Math. Notes 7, 194-196, 1970. https://doi.org/10.1007/BF01093113.

Cite this as:

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

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