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Hall-Janko Near Octagon

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The Hall-Janko near octagon, also known as the Cohen-Tits near octagon, is a weakly regular graph on 315 vertices with parameters (n,k,lambda,mu)=(315,(10),(1),(0,1)). It is distance-regular with intersection array {10,8,8,2;1,1,4,5} and also distance-transitive.

It has graph spectrum (-5)^(28)(-2)^(160)3^(90)5^(36)10^1 and so is an integral graph. The Janko group J2 acts on the graph, realizing it as a subgroup of the full graph automorphism group (Brouwer et al. 1989). The full group is denoted J_2.2 and has group order Aut(G)=1209600 (DistanceRegular.org). Since J_2 has group order 604800, it has index 2 in the full group.

It is a Hamiltonian graph.

The Hall-Janko near octagon is implemented in the Wolfram Language as GraphData["HallJankoNearOctagon"].

See also

Distance-Regular Graph, Distance-Transitive Graph, Janko Group J2

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References

Brouwer, A. E. "The Cohen-Tits Near Octagon on 315 Points." https://aeb.win.tue.nl/drg/graphs/HJ315.html.Brouwer, A. E.; Cohen, A. M.; and Neumaier, A. Distance-Regular Graphs. New York: Springer-Verlag, pp. 408-410, 1989.Cohen, A. M. "Geometries Originating from Certain Distance-Regular Graphs." In Proc. Finite Geometries and Designs. Cambridge, England: Cambridge University Press, pp. 81-87, 1981.Cohen, A. M. and Tits, J. "On Generalized Hexagons and a Near Octagon Whose Lines Have Three Points." Europ. J. Combin. 6, 13-27, 1985.DistanceRegular.org. "Hall-Janko Near Octagon from J_2.2 = Cohen-Tits Near Octagon." https://www.math.mun.ca/distanceregular/graphs/halljanko315.html.

Referenced on Wolfram|Alpha

Hall-Janko Near Octagon

Cite this as:

Weisstein, Eric W. "Hall-Janko Near Octagon." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/Hall-JankoNearOctagon.html

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