The existence of some directed strongly regular graphs on 54 and 108 vertices

Abstract

In this paper, we prove the existence of directed strongly regular graphs with parameters (108,11,3,2,1), (108,14,10,0,2), (108,22,12,6,4), (108,23,9,8,4), (108,25,15,8,5), (108,34,18,12,10), (108,38,22,12,14), (108,39,23,14,14), (108,41,35,16,15), (108,42,33,18,15) and (108,46,22,19,20). Further, we obtain directed strongly regular graphs with parameters (54,10,4,1,2), (54,11,4,3,2) and (54,16,7,4,5). The constructions are obtained by considering finite groups acting transitively on 54 and 108 vertices.

8 pages