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 |  |
