半群Cayley图的传递性

On Transitivity of Cayley Graphs of Semigroups

主要研究了半群Cayley图的传递性.得到了完全单半群的Cayley图的弱点传递性的等价条件,给出了半群的Cayley图是自同构弧传递的充分必要条件,特别地,完全刻画了带的Cayley图的自同构弧传递条件.

The transitivity of Cayley graphs of semigroups is mainly dealed with in this paper. Firstly, we obtain some equivalent characterization for Cayley graphs of completely simple semigroup which is vertextransitive. Secondly, we study the arc-transitive Cayley graphs of semigroups, and give a necessary and suf- ficient condition for Cayley graphs of semigroups which are arc-transitive under suitable conditions. Finally,we get a complete description of all arc-transitive Cayley graphs of bands.