有限非交换单群上的10度1-正则Cayley图

On 10-Valent 1-Regular Cayley Graphs on Finite Nonabelian Simple Groups

称Cayley图Γ=Cay(G,S)是1-正则的,如果的全自同构群Aut(Γ)作用在其弧集上正则。称Γ是正规的,如果G◁Aut(Γ)。在本文中, 我们证明了有限非交换单群上的连通10度1-正则Cayley图一定是正规的。

A Cayley graph Γ=Cay(G,S) is said to be 1-regular, if the full automorphism group Aut(Γ) of Γ acts regularly on the arc set of Γ. And Γ is called normal if G◁Aut(Γ). In this paper, we prove 10-valent 1-regular Cayley graphs on finite nonabelian simple groups must be normal.