Automorphisms of distance-regular graph with intersection array {24,18,9;1,1,16}

摘要

Koolen and Park classified Shilla graphs with b = 2 andwith b = 3. Prime divisors of orders of automorphisms and the fixedpoint subgraphs of automorphisms of prime orders are studied for ahypothetical distance-regular graph Γ with intersection array f24; 18; 9; 1;1; 16g. Let G = Aut(Γ) is nonsolvable group, ˉG = G=S(G) and ˉ T is thesocle of ˉ G. Then G contains now elements of order 35 and ˉ T =J2;A10or Ω+8 (2). In particular graph Γ is not vertex symmetric.