非交换单群上三度点传递双凯莱图

Cubic Vertex-transitive Bi-cayley Graphs Over Non-abelian Simple Groups

如果一个图Γ含有一个自同构群G使得它在顶点集V(Γ)上作用半正则且恰好有两个轨道,则称图Γ是群G上的双凯莱图.进一步的,如果G在全自同构群Aut(Γ)中正规,我们就称这个双凯莱图是群G上的正规双凯莱图.本文中,我们证明了绝大多数非交换单群G上的三度点传递双凯莱图都是该群上的正规双凯莱图.

A graphΓis said to be a bi-Cayley graph over a group G ifΓhas an automorphism group isomorphic to G and acts semiregularly on V(Γ)with exactly two orbits.Furthermore,if G is normal in the full automorphism group ofΓ,thenΓis said to be a normal bi-Cayley graph over G.In this paper,we prove that for all most non-abelain simple groups G,cubic vertex-transitive bi-Cayley graphs over G are normal bi-Cayley graphs over G.