【摘要】 令Γ是一个图,如果Γ的自同构群Aut(Γ)作用在其弧集上是正则的,则称图Γ为1-正则图。在本文中,奇素数度1-正则Cayley图被完全分类,得到如下结论:一个奇素数度1-正则Cayley图要么是双正规的双Cayley图,要么在同构意义下是已知的6类无核Cayley图的正规覆盖:3个无限类、3个零散图,其中包括2个11度图以及1个23度图。更多还原

【Abstract】 A graphΓis called 1-regular if Aut(Γ)acts regularly on its arcs.In this paper,the 1-regular Cayley graphs of valency odd prime is classified completely,and the following conclusions are obtained:a 1-regular Cayley graph of valency odd prime is either a bi-normal bi-Cayley graph or a normal covering of the known six types of core-free ones up to isomorphism,which are three infinite types,three scattered graphs,including two graphs of valency 11 and a graph of valency 23.更多还原