Enumeration of Strongly Regular Graphs on up to 50 Vertices Having S3 as an Automorphism Group

One of the main problems in the theory of strongly regular graphs (SRGs) is constructing and classifying SRGs with given parameters. Strongly regular graphs with parameters (37,18,8,9), (41,20,9,10), (45,22,10,11), (49,24,11,12), (49,18,7,6) and (50,21,8,9) are the only strongly regular graphs on up to 50 vertices that still have to be classified. In this paper, we give the enumeration of SRGs with these parameters having S3 as an automorphism group. The construction of SRGs in this paper is a step in the classification of SRGs on up to 50 vertices.