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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.

ngraphintersection array
6cycle graph C_6{2,1,1;1,1,2}
8cubical graph Q_3{3,2,1;1,2,3}
12icosahedral graph{5,2,1;1,2,5}
206-tetrahedral Johnson graph J(6,3){9,4,1;1,4,9}
28locally 13-Paley graph{13,6,1;1,6,13}
326-halved cube graph{15,6,1;1,6,15}
28locally 17-Paley graph{17,8,1;1,8,17}
32locally Kneser graph K(6,2){15,8,1;1,8,15}
56Gosset graph{27,10,1;1,10,27}
56distance-2 graph of Gosset graph{27,16,1;1,16,27}
352graph from Higman-Sims group 1{175,102,1;1,102,175}
352graph from Higman-Sims group 2{175,72,1;1,72,175}
552graph from Conway group Co_3 1{275,112,1;1,112,275}
552graph 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.

Referenced on Wolfram|Alpha

Taylor Graph

Cite this as:

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

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