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.

CEMAT - Center for Computational and Stochastic Mathematics