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Automorphisms of Endomorphism Semigroups of Reflexive Digraphs

Araújo, João; Dobson, Edward; Konieczny, Janusz

Mathematische Nachrichten, 283(7) (2010), 1-26

A reflexive digraph is a pair (X, ?), where X is an arbitrary set and ? is a reflexive binary relation on X. Let End (X, ?) be the semigroup of endomorphisms of (X, ?). We determine the group of automorphisms of End (X, ?) for: digraphs containing an edge not contained in a cycle, digraphs consisting of arbitrary unions of cycles such that cycles of length ?2 are pairwise disjoint, and some circulant digraphs.