The Wong graph is one of the four 
-cage graphs. Like the other
-cages,
the Wong graph has 30 nodes. It has 75 edges,
girth 5, graph diameter
3, chromatic number 4, and is a quintic
graph. Note that the graph depicted in Bondy and Murty
(1976, p. 238) and labeled "
-cage: The Robertson-Wegner graph" (and shown above)
is actually the Wong graph.
The Wong graph has LCF notation signature 
, and is illustrated at the top in its
two order-10 LCF drawings and above in its seven order-5 LCF drawings.
The Wong graph is implemented in the Wolfram Language as GraphData["WongGraph"].
The Wong graph has graph spectrum 
.
Its automorphism group is of group
order 120.
The Wong graph satisfies the rhombus constraints and contains no known unit-distance forbidden subgraph, yet appears not to be a unit-distance graph. A number of drawings found from different initial drawings by minimizing the sum of squared deviations from unit edge lengths until a local minimum was reached are illustrated above.
