A Characterization of Cayley Graphs of Brandt Semigroups

In this paper, first we characterize Cayley graphs of finite Brandt semigroups,and we give a criterion to check whether a finite digraph is a Cayley graph of a finite Brandt semigroup. Also Kelarev and Praeger gave necessary and sufficient conditions for Cayley graphs of semigroups to be vertex-transitive. Then, some authors gave descriptions for all vertex-transitive Cayley graphs of some special classes of semigroups. In this note similar descriptions for all vertex-transitive Cayley graphs of Brandt semigroups are given.