Abstract
In this paper, the Cayley graphs of completely simple semigroups are investigated. The basic structure and properties of this kind of Cayley graph are given, and a condition is given for a Cayley graph of a completely simple semigroup to be a disjoint union of complete graphs. We also describe all pairs (S,A) such that S is a completely simple semigroup, A⊆S, and Cay (S,A) is a strongly connected bipartite Cayley graph.
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