Strongly regular graphs with parameters (37, 18, 8, 9) having nontrivial automorphisms

Keywords: Strongly regular graph, automorphism group, orbit matrix


All strongly regular graphs having at most 36 vetrices have been enumerated. Hence, the first open case is enumeration of the SRGs with parameters (37,18,8,9). In this paper we show that there are exactly forty SRGs with parameters (37,18,8,9) having nontrivial automorphisms. Comparing the constructed graphs with previously known SRGs with these parameters we conclude that six of the SRGs with parameters (37,18,8,9) constructed in this paper are new, and that up to isomorphism there are at least 6766 strongly regular graphs with parameters (37,18,8,9).

Author Biography

Dean Crnković, University of Rijeka, Croatia

Department of Mathematics