On Cayley graphs of generalized Brandt semigroups

The Cayley graphs of generalized Brandt semigroups whose connection sets are Green equivalence classes are investigated. The structures of the Cayley graphs of generalized Brandt semigroups with the Green equivalent classes (L-class, R-class and H-class) as the connection sets are depicted, and the essential characteristic of generalized Brandt semigroup is exactly a complete 0-simple orthodox semigroup is revealed, by studying respectively isomorphic conditions between these Cayley graphs.