Heptavalent Symmetric Graphs with Certain Conditions

• 作者: Jiali Du Yanquan Feng Yuqin Liu
• 来源期刊: 代数集刊（英文版）
• 年，卷（期）: 2021,（2）
• 页码范围: 243-252
• 页数: 10页
• 语种: 英文
• DOI: 10.1142/S1005386721000195

摘要

A graph Γ is said to be symmetric if its automorphism group Aut(Γ)acts transitively on the arc set of Γ.We show that if Γ is a finite connected heptavalent symmetric graph with solvable stabilizer admitting a vertex-transitive non-abelian simple group G of automorphisms,then either G is normal in Aut(Γ),or Aut(Γ)contains a non-abelian simple normal subgroup T such that G≤T and(G,T)is explicitly given as one of 11 possible exceptional pairs of non-abelian simple groups.If G is arc-transitive,then G is always normal in Aut(r),and if G is regular on the vertices of Γ,then the number of possible exceptional pairs(G,T)is reduced to 5.