A generalized hexagon is a generalized polygon of order 6.
is more commonly known as the Heawood graph, but is also the -cage graph, the cubic vertex-transitive graph Ct15, the cubic symmetric graph , the 69-Haar graph, and is an incidence graph of a 2- design.
is the -cage graph, 4137-Haar graph, and is an incidence graph of a 2- design.
is the Bouwer graph , line graph of the Heawood graph, and is a distance-regular graph with intersection array ,
is the line graph of the -cage, is also known as the flag graph of (DistanceRegular.org), and is a distance-regular graph with intersection array .
is the line graph of the -cage, is also known as the flag graph of (DistanceRegular.org), and is the distance-regular graph with intersection array .
The generalized hexagons are line graphs of the generalized hexagons .
The following table summarizes some generalized hexagons.
graph | other names | incidence | graph spectrum | |
GH(1, 2) | 14 | Heawood graph | ||
GH(1, 3) | 26 | (4, 6)-cage graph, incidence graph of | ||
GH(1, 4) | 42 | (5, 6)-cage graph | ||
GH(1, 5) | 62 | (6, 6)-cage graph | ||
GH(1, 7) | 114 | (8, 6)-cage graph | ||
GH(1, 8) | 146 | (9, 6)-cage graph | ||
GH(1, 9) | 182 | (10, 6)-cage graph | ||
GH(2, 1) | 21 | (2,3,7)-Bouwer graph, flag graph of | ||
GH(2, 8) | 819 | |||
GH(3, 1) | 52 | |||
GH(4, 1) | 105 | |||
GH(5, 1) | 186 | |||
GH(7, 1) | 456 | |||
GH(8, 1) | 657 | |||
GH(8, 2) | 2457 |