2024/03/02 by Fang, Teng, Zhou, Sanming, Zhou, Shenglin
#05C25 #05E18 #Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.2403.01324
A graph Γ is G-symmetric if it admits G as a group of automorphisms acting transitively on the set of arcs of Γ, where an arc is an ordered pair of adjacent vertices. Let Γ be a G-symmetric graph such that its vertex set admits a nontrivial G-invariant partition \cal B, and let \cal D(Γ, \cal B) be the incidence structure with point set \cal B and blocks \B\ ∪ Γ\cal B(α), for B ∈ \cal B and α∈ B, where Γ\cal B(α) is the set of blocks of \cal B containing at least one neighbour of α in Γ. In this paper we classify all G-symmetric graphs Γ such that Γ\cal B(α) ≠ Γ\cal B(β) for distinct α, β∈ B, the quotient graph of Γ with respect to \cal B is a complete graph, and \cal D(Γ, \cal B) is isomorphic to the complement of a (G, 2)-point-transitive linear space.