Edge-transitive core-free Nest graphsKovács, István (Avtor) bicirculantedge-transitiveprimitive permutation groupA finite simple graph Γ is called a Nest graph if it is regular of valency 6 and admits an automorphism ρ with two orbits of the same length such that at least one of the subgraphs induced by these orbits is a cycle. We say that Γ is core-free if no non-trivial subgroup of the group generated by ρ is normal in Aut(Γ). In this paper, we show that, if Γ is edge-transitive and core-free, then it is isomorphic to one of the following graphs: the complement of the Petersen graph, the Hamming graph H(2,4), the Shrikhande graph and a certain normal 2-cover of K_{3,3} by ℤ_2^4.Založba Univerze na Primorskem20252025-09-10 13:32:38Neznano21707sl