It can be constructed as follows. There is a unique 56-cap in (i.e., the set of 56 points such that any line meets
it in at most two points) (Hill 1978). Taking the as vertices the points of 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, Games pers. comm. to Brouwer and van Lint 1984).
Bondarenko, A. V. and Radchenko, D. V. "On a Family of Strongly Regular Graphs with ." J. Combin. Th. (B)103, 521-531,
2013.Brouwer, A. E. and van Lint, J. H. "Strongly Regular
Graphs and Partial Geometries." In Enumeration
and Design: Papers from the Conference on Combinatorics Held at the University of
Waterloo, Waterloo, Ont., June 14-July 2, 1982 (Ed. D. M. Jackson
and S. A. Vanstone). Toronto, Canada: Academic Press, pp. 85-122,
1984.Brouwer, A. E. and van Maldeghem, H. "The Games Graph."
§10.75 in Strongly
Regular Graphs. Cambridge, England: Cambridge University Press, p. 354-355,
2022.Cameron, P. J. "Partial Quadrangles." Quart.
J. Math. Oxford26, 61-73, 1975.DistanceRegular.org. "Games
graph." https://www.distanceregular.org/graphs/games.html.Games,
R. A. "The Packing Problem for Finite Projective Geomeries." Ph.D.
Thesis. Columbus, OH: Ohio State Univ., pp. 171 and 329, 1980.Hill,
R. "Caps and Codes." Discr. Math.22, 111-137, 1978.
.
and has graph spectrum 
.
(i.e., the set of 56 points such that any line meets
it in at most two points) (Hill 1978). Taking the as vertices the points of 
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, Games pers. comm. to 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