Combinatorial Theory

The intersection density of a transitive permutation group \(G\leq \operatorname{Sym}(V)\) is the ratio between the largest size of a subset of \(G\) in which any two agree on at least one element of \(V\), and the order of a point-stabilizer of \(G\). In this paper, we determine the intersection densities of the automorphism groups of the arc-transitive graphs admitting a \(2\)-arc-regular full automorphism group \(G^* = \operatorname{PGL}_{2}(q)\) and an arc-regular subgroup of automorphism \(G = \operatorname{PSL}_{2}(q)\).

Mathematics Subject Classifications: 05C35, 05C69, 20B05

Keywords: Derangement graphs, cocliques, projective special linear groups