Some new symmetric designs with parameters (64,28,12)

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

“…Orbit matrices of block designs have been frequently used for the construction of block designs with a presumed automorphism group, see, e.g., [8][9][10][11]. In 2011, Behbahani and Lam introduced the concept of orbit matrices of SRGs (see [4]).…”

“…SRGs 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 [2,15]. According to [2], it is known that strongly regular graphs with these parameters exist, but their final enumeration result is not known.…”

“…According to [2], it is known that strongly regular graphs with these parameters exist, but their final enumeration result is not known. In this section, we present the results of the constructed strongly regular graphs with parameters (37, 18,8,9), (41, 20, 9, 10), (45, 22, 10, 11), (49, 18,7,6), (49,24,11,12) and (50, 21,8,9) having S 3 ∼ = Z 3 : Z 2 ∼ = ρφ|ρ 3 = 1, φ 2 = 1, φρφ = ρ −1 as an automorphism group. In each case, we construct strongly regular graphs by using the algorithm described in Section 3.…”

“…Using this method, we classify strongly regular graphs with parameters (37, 18,8,9), (41, 20, 9, 10), (45, 22,10,11), (49,18,7,6), (49,24,11,12) and (50, 21,8,9) having S 3 as an automorphism group. These graphs are the only strongly regular graphs with up to 50 vertices that still have to be classified.…”

“…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 S 3 as an automorphism group.…”