The Harries-Wong graph is one of the three -cage graphs, the other two being the -cage known as the Balaban 10-cage and the Harries graph.
The Harries-Wong graph is Hamiltonian with Hamiltonian cycles. It has distinct LCF notations, all of order 1, and one of which is given by [9, 25, 31, , 17, 33, 9, , , , 9, 25, , 29, 17, , 9, , 35, , 9, , 21, 27, , , , 13, 19, , , , 19, , 27, 11, , 29, , 13, , 21, , , 25, 9, , , 29, 9, , , , , , 9, 17, 25, , 9, 27, , , 15, , 29, , 33, , ].
The plots above show the adjacency matrix, incidence matrix, and graph distance matrix for the Harries-Wong graph.
The Harries-Wong graph are cospectral graphs, meaning neither is determined by spectrum.
The following table summarizes properties of the Harries-Wong graph.
automorphism group order | 24 |
characteristic polynomial | |
chromatic number | 2 |
claw-free | no |
clique number | 2 |
cospectral graph names | Harries graph |
determined by spectrum | no |
diameter | 6 |
distance-regular graph | no |
edge chromatic number | 3 |
edge connectivity | 3 |
edge count | 105 |
Eulerian | no |
girth | 10 |
Hamiltonian | yes |
Hamiltonian cycle count | 94656 |
integral graph | no |
independence number | 35 |
perfect matching graph | no |
planar | no |
polyhedral graph | no |
radius | 6 |
regular | yes |
square-free | yes |
traceable | yes |
triangle-free | yes |
vertex connectivity | 3 |
vertex count | 70 |
weakly regular parameters |