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# Generalized Dodecagon

A generalized dodecagon is a generalized polygon of order 12.

is the -cage graph, more commonly known as the Tutte 12-cage.

is the line graph of the Tutte 12-cage and is a distance-regular graph with intersection array .

is a -cage graph and incident graph of the generalized hexagon (DistanceRegular.org). It is also a distance-transitive graph with intersection array .

The following table summarizes some generalized dodecagons.

 graph other names graph spectrum 126 189 flag graph of 728 (4,12)-cage graph, incidence graph of 132860

Cage Graph, Generalized Hexagon, Generalized Polygon, Generalized Quadrangle, Tutte 12-Cage

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## References

Brouwer, A. E.; Cohen, A. M.; and Neumaier, A. Distance-Regular Graphs. New York: Springer-Verlag, p. 204, 1989.DistanceRegular.org. "Incidence Graph of GH(3,3)." http://www.distanceregular.org/graphs/incidence-gh3.3.html.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 Dodecagon

## Cite this as:

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