The Games graph is a strongly regular graph on 729 vertices with parameters 
.
It is distance-regular but not distance-transitive with intersection
array 
and has graph spectrum 
.
It is implemented in the Wolfram Language as GraphData["GamesGraph"].
It can be constructed as follows. There is a unique 56-cap in the projective space 
(i.e., the set of 56 points such
that any line meets it in at most two points)
(Hill 1978). Taking as vertices the points
of the affine space 
and joining two vertices
when the line through the points
meets the hyperplane at infinity in a point
of the cap gives the Games graph (Cameron 1975; R. A. Games, as reported
by Brouwer and van Lint 1984).
." J. Combin. Th. (B) 103, 521-531,
2013.Brouwer, A. E. and van Lint, J. H. "Strongly Regular
Graphs and Partial Geometries." In