Taylor Graph

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A Taylor graph is a distance-regular graph with intersection array {k,mu,1;1,mu,k}. A Taylor graph with these parameters has 2(k+1) vertices.

The crown graphs K_2 square K_n^_ are Taylor graphs with intersection arrays {n-1,n-2,1;1,n-2,n-1}.

TaylorGraphs

A number of other Taylor graphs are summarized below and illustrated above.

n graph intersection array

6 cycle graph C_6 {2,1,1;1,1,2}

8 cubical graph Q_3 {3,2,1;1,2,3}

12 icosahedral graph {5,2,1;1,2,5}

20 6-tetrahedral Johnson graph J(6,3) {9,4,1;1,4,9}

28 locally 13-Paley graph {13,6,1;1,6,13}

32 6-halved cube graph {15,6,1;1,6,15}

28 locally 17-Paley graph {17,8,1;1,8,17}

32 locally Kneser graph K(6,2) {15,8,1;1,8,15}

56 Gosset graph {27,10,1;1,10,27}

56 distance-2 graph of Gosset graph {27,16,1;1,16,27}

352 graph from Higman-Sims group 1 {175,102,1;1,102,175}

352 graph from Higman-Sims group 2 {175,72,1;1,72,175}

552 graph from Conway group Co_3 1 {275,112,1;1,112,275}

552 graph from Conway group Co_3 2 {275,162,1;1,162,275}

See also

Distance-Regular Graph, Intersection Array

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References

Brouwer, A. E.; Cohen, A. M.; and Neumaier, A. Distance Regular Graphs. New York: Springer-Verlag, pp. 13, 33, 225, and 228, 1989.DistanceRegular.org. "Taylor Graphs." http://www.distanceregular.org/indexes/taylorgraphs.html.

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Cite this as:

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

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