order 1296. It acts transitively on the edges the graph but not on its vertices : there are symmetries taking every edge to any other edge, but not taking every vertex to any other vertex. The vertices that correspond to points of the underlying configuration can only be symmetric to other vertices that correspond to points, and the vertices that correspond to lines can only be symmetric to other vertices that correspond to lines. Therefore, the Gray graph is a semi-symmetric graph, the smallest possible cubic semi-symmetric graph. The characteristic polynomial of the Gray graph is References . . . . . External links The Gray Graph Is the Smallest Graph of Its Kind, from MathWorld. Configurations (geometry) Individual graphs Regular graphs