2016/05/11 by Teng Fang, Xin Fang, Fang, Teng +5
Computer Science · Engineering · Mathematics · #Coding theory and cryptography #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.1605.03530
openalex publication_date 2016/05/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A graph Γ is called G-symmetric if it admits G as a group of automorphisms acting transitively on the set of ordered pairs of adjacent vertices. We give a classification of G-symmetric graphs Γ with V(Γ) admitting a nontrivial G-invariant partition B such that there is exactly one edge of Γ between any two distinct blocks of B. This is achieved by giving a classification of (G, 2)-point-transitive and G-block-transitive designs D together with G-orbits Ω on the flag set of D such that Gσ, L is transitive on L ∖ \σ\ and L ∩ N = \σ\ for distinct (σ, L), (σ, N) ∈ Ω, where Gσ, L is the setwise stabilizer of L in the stabilizer Gσ of σ in G. Along the way we determine all imprimitive blocks of Gσ on V ∖ \σ\ for every 2-transitive group G on a set V, where σ∈ V.