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Let <jats:italic>End<\/jats:italic> (<jats:italic>X<\/jats:italic>, <jats:italic>\u03c1<\/jats:italic>) be the semigroup of endomorphisms of (<jats:italic>X<\/jats:italic>, <jats:italic>\u03c1<\/jats:italic>). We determine the group of automorphisms of <jats:italic>End<\/jats:italic> (<jats:italic>X<\/jats:italic>, <jats:italic>\u03c1<\/jats:italic>) for: digraphs containing an edge not contained in a cycle, digraphs consisting of arbitrary unions of cycles such that cycles of length \u22652 are pairwise disjoint, and some circulant digraphs (\u00a9 2010 WILEY\u2010VCH Verlag GmbH &amp; Co. KGaA, Weinheim)<\/jats:p>","DOI":"10.1002\/mana.200710033","type":"journal-article","created":{"date-parts":[[2010,5,12]],"date-time":"2010-05-12T19:22:00Z","timestamp":1273692120000},"page":"939-964","source":"Crossref","is-referenced-by-count":3,"title":["Automorphisms of endomorphism semigroups of reflexive digraphs"],"prefix":"10.1002","volume":"283","author":[{"given":"Jo\u00e3o","family":"Ara\u00fcjo","sequence":"first","affiliation":[]},{"given":"Edward","family":"Dobson","sequence":"additional","affiliation":[]},{"given":"Janusz","family":"Konieczny","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2010,6,22]]},"reference":[{"key":"e_1_2_1_2_2","unstructured":"M. E.Adams S.Bulman\u2010Fleming andM.Gould Endomorphism properties of algebraic structures in: Proceedings of the Tennessee Topology Conference Nashville TN 1996 (World Sci. 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