The Harries-Wong graph is one of the three 
-cage graphs, the other
two being the 
-cage graph known as the Balaban
10-cage and the Harries graph.
The Harries-Wong graph is implemented in the Wolfram Language as GraphData["HarriesWongGraph"].
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 and Harries graph are cospectral graphs, meaning neither is determined by spectrum.
The following table summarizes properties of the Harries-Wong graph.
