On Symmetric Cayley Graphs of Valency Eleven

• 作者: Bo Ling Bengong Lou Li Ma Xue Yu
• 来源期刊: 代数集刊（英文版）
• 年，卷（期）: 2021,（2）
• 页码范围: 309-318
• 页数: 10页
• 语种: 英文
• DOI: 10.1142/S1005386721000249

摘要

A Cayley graph Γ=Cay(G,S)is said to be normal if G is normal in Aut Γ.In this paper,we investigate the normality problem of the connected 11-valent symmetric Cayley graphs Γ of finite nonabelian simple groups G,where the vertex stabilizer Av is soluble for A=Aut Γ and v ∈ VΓ.We prove that either Γ is normal or G=A5,A10,A54,A274,A549 or A1099.Further,11-valent symmetric nonnormal Cayley graphs of A5,A54 and A274 are constructed.This provides some more examples of nonnormal 11-valent symmetric Cayley graphs of finite nonabelian simple groups after the first graph of this kind(of valency 11)was constructed by Fang,Ma and Wang in 2011.