它可以如下构造。在 中存在唯一的 56-cap(即,任何线最多与其相交于两点的 56 个点的集合)(Hill 1978)。将 中的点作为顶点,当通过这些点的线在无穷远处的超平面上与 cap 中的点相交时,连接两个顶点,得到 Games 图 (Cameron 1975, Games 私人通讯给 Brouwer 和 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.