Geodesic
Characterization of finite simple semigroup digraphs
Algebra and discrete mathematics, Tome 12 (2011) no. 1, pp. 53-68.

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This paper characterizes directed graphs which are Cayley graphs of finite simple semigroups, i.e. of a subspecies of completely regular semigroups. Moreover we investigate the structure of Cayley graphs of finite simple semigroups with a one-element connection set. We introduce the conditions for which they are isomorphic and connected.
Keywords: Cayley graph, digraph, completely regular, completely simple semigroups, Rees matrix semigroup. 
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J. Meksawang; S. Panma; U. Knauer. Characterization of finite simple semigroup digraphs. Algebra and discrete mathematics, Tome 12 (2011) no. 1, pp. 53-68. http://geodesic.mathdoc.fr/item/ADM_2011_12_1_a3/

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