2023/08/06 by Cesarz, Patrick G., Woldar, Andrew J.
#05E18 #Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.2308.02978
Let Γ be a Conway 99-graph, that is, a strongly regular graph with parameters (99,14,1,2). In Makhnev and Minakova (On automorphisms of strongly regular graphs with parameters λ=1, μ= 2, Discrete Math. Appl. 14 (2) (2004) 201-210), the authors prove that the automorphism group G of Γ must have order dividing 2⋅ 33⋅ 7⋅ 11. They further show that if |G| is divisible by 2 then |G| must divide 42. In the present paper, we refine these results by proving that divisibility by 7 implies G ≅\mathbb Z7. As a consequence, divisibility by 2 implies |G| divides 6, \ie G is isomorphic to one of \mathbb Z2, \mathbb Z6, S3.