Volume 35 • Number 2 • 2012   • A Characterization of Cayley Graphs of Brandt Semigroups Behnam Khosravi and Bahman Khosravi Abstract. 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. 2010 Mathematics Subject Classification: Primary 05C25, 05C75; Secondary 05C20. Full text: PDF