The Hall-Janko graph, also known as the Hall-Janko-Wales graph, is a strongly regular graph on 100 vertices with parameters
. It is also a distance-regular
graph with intersection array 
, as well as being distance-transitive.
It is illustrated above in a graph drawing due to C. Rocchini.
It is an integral graph with graph spectrum 
. The Hall-Janko graph has independence
number 10 and chromatic number 10, while
the graph complement of the Hall-Janko graph
has independence number 4 and chromatic
number 25 (Brouwer).
The Janko group J2 acts on the graph, realizing it as a subgroup
of the full automorphism group (Hall and
Wales 1968). The full group is denoted 
and has group order 
(DistanceRegular.org). Since 
has group
order 
, it has index
2 in the full group.
It is implemented in the Wolfram Language as GraphData["HallJankoGraph"].
It is the middle graph in the chain of local graphs known as the Suzuki tower.
