The Harries graph is one of the three -cage graphs, the other two being the -cage known as the Balaban 10-cage and the Harries-Wong graph.
The Harries graph is Hamiltonian with Hamiltonian cycles. It has 678 distinct LCF notations, four of which are order 5 (illustrated above) and 674 of which are order 1. The order-5 LCF notations are [, , and .
The plots above show the adjacency matrix, incidence matrix, and graph distance matrix for the Harries graph.
Notice that the Harries graph and Harries-Wong graph are cospectral graphs, meaning neither is determined by spectrum.
The following table summarizes properties of the Harries graph.
automorphism group order | 120 |
characteristic polynomial | |
chromatic number | 2 |
claw-free | no |
clique number | 2 |
cospectral graph names | Harries-Wong 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 | 98304 |
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 |