Some Studies On Cayley Graphs Of Semigroups

This thesis mainly deals with some properties on Cayley graphs of semigroups. The whole thesis consists of three chapters.In Chapter 1, some research backgrounds are introduced.In Chapter 2, we chiefly study Cayley graphs of strong semilattices of left (right) groups and obtain some results for structures and properties of these graphs. Meanwhile, a sufficient condition is established for which a digraph with certain properties is the Cayley graphs of strong semilattices of left (right) groups. Furthermore, we can have the corresponding results for Cayley graphs of Clifford semigroups if left (right) groups are restricted to groups. Therefore, the conclusions in the chapter extend the main theorems in [5].Chapter 3 is mainly concerned with transitivity of Cayley graphs of semigroups. Firstly, we obtain some equivalent characterizations for Cayley graphs of completely simple semigroup which are End_s(G)-vertex-transitive. Secondly, we study the arc-transitive of Cayley graphs of semigroups, and give a necessary and sufficient condition for Cayley graphs of semigroups which are Aut_s(G)-arc transitive under suitable conditions. Finally, we get a complete description of all arc-transitive Cayley graphs of bands.