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Egawa Graph

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The Egawa graph with parameters (p,s) is a distance-regular but not distance-transitive graph on 16^p4^s nodes. These graphs generalize the Doob graphs and give (s,4)-Hamming graphs when p=0.

Egawa graphs are implemented in the Wolfram Language as GraphData[{"Egawa", {p, s}}].

Special cases are summarized in the following table.

(p,s)graph
(0,0)singleton graph K_1
(0,1)tetrahedral graph K_4
(0,2)rook graph K_4×K_4
(0,s)(s,4)-Hamming graph
(1,2)Shrikhande graph
(p,s) with p>0(p,s)-Doob graph

See also

Distance-Regular Graph, Doob Graph, Hamming Graph

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References

Egawa, Y. "Characterization of H(n,q) by the Parameters." J. Combin. Th., Ser. A 31, 108-125, 1981.

Cite this as:

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

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