On automorphisms of a distance-regular graph with intersection array {243, 220, 1; 1, 22, 243}
It was proved that a distance-regular graph in which neighborhoods of vertices are strongly regular with parameters (245,64,18,16) has intersection array {243, 220,1; 1, 22, 243} or {243, 220,1; 1,4, 243}. In this paper we found the automorphisms of a distance regular graph with intersection array {243, 220, 1; 1, 22, 243}. It is proved that a vertex-transitive distance-regular graph with intersection array {243, 220,1; 1, 22, 243} is the arc-transitive Mathon graph affording the group L<sub>2</sub>(3<sup>5</sup>).