in graph theory, the games graph is the largest known locally linear strongly regular graph. its parameters as a strongly regular graph are (729,112,1,20). this means that it has 729 vertices, and 40824 edges (112 per vertex). each edge is in a unique triangle (it is a locally linear graph) and each non-adjacent pair of vertices have exactly 20 shared neighbors. it is named after richard a. games, who suggested its construction in an unpublished communication and wrote about related constructions.