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Generalized Octagon

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A generalized octagon GO(n,k) is a generalized polygon of order 8.

GO(1,2) is the (3,8)-cage graph, the incidence graph of the Cremona-Richmond configuration, the cubic vertex-transitive graph Ct63, the cubic symmetric graph F_(030)A, and is also sometimes known as the Tutte 8-cage.

GO(2,1) is the line graph of the Tutte 8-cage.

The following table summarizes some generalized octagons.

graphVnameother namesgraph spectrum
GO(1, 2)30Tutte 8-cage(-3)^1(-2)^90^(10)2^93^1
GO(1, 3)80(4, 8)-cage graph(-4)^1(-sqrt(6))^(24)0^(30)(sqrt(6))^(24)4^1
GO(1, 4)180(5, 8)-cage graph(-5)^1(-2sqrt(2))^(50)0^(68)(2sqrt(2))^(50)5^1
GO(1, 8)1170(9, 8)-cage graph(-9)^1(-4)^(324)0^(520)4^(324)9^1
GO(2, 1)45flag graph of GQ(2,2)(-2)^(16)(-1)^91^(10)3^94^1
GO(3, 1)160(-2)^(81)(2-sqrt(6))^(24)2^(30)(2+sqrt(6))^(24)6^1
GO(4, 1)425(-2)^(256)(3-sqrt(8))^(50)3^(68)(3+sqrt(8))^(50)8^1

See also

Generalized Dodecagon, Generalized Hexagon, Generalized Polygon, Generalized Quadrangle

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References

Brouwer, A. E.; Cohen, A. M.; and Neumaier, A. Distance-Regular Graphs. New York: Springer-Verlag, p. 204, 1989.van Dam, E. R. and Haemers, W. H. "Which Graphs Are Determined by Their Spectrum?" Lin. Algebra Appl. 373, 139-162, 2003.

Referenced on Wolfram|Alpha

Generalized Octagon

Cite this as:

Weisstein, Eric W. "Generalized Octagon." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/GeneralizedOctagon.html

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