Geodesic
Cayley color graphs of inverse semigroups and groupoids
Czechoslovak Mathematical Journal, Tome 58 (2008) no. 3, pp. 683-692.

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The notion of Cayley color graphs of groups is generalized to inverse semigroups and groupoids. The set of partial automorphisms of the Cayley color graph of an inverse semigroup or a groupoid is isomorphic to the original inverse semigroup or groupoid. The groupoid of color permuting partial automorphisms of the Cayley color graph of a transitive groupoid is isomorphic to the original groupoid.
Classification : 20B25, 20M18
Keywords: Cayley color graph; inverse semigroup; groupoid 
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     title = {Cayley color graphs of inverse semigroups and groupoids},
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Sieben, Nándor. Cayley color graphs of inverse semigroups and groupoids. Czechoslovak Mathematical Journal, Tome 58 (2008) no. 3, pp. 683-692. http://geodesic.mathdoc.fr/item/CMJ_2008__58_3_a6/