{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,11]],"date-time":"2026-03-11T13:59:54Z","timestamp":1773237594336,"version":"3.50.1"},"reference-count":29,"publisher":"Walter de Gruyter GmbH","issue":"5","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2024,10,28]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>In this paper, we consider endomorphisms of an undirected cycle graph from Semigroup Theory perspective. Our main aim is to present a process to determine sets of generators with minimal cardinality for the monoids wEnd<jats:italic>C<jats:sub>n<\/jats:sub>\n                  <\/jats:italic> and End<jats:italic>C<jats:sub>n<\/jats:sub>\n                  <\/jats:italic> of all weak endomorphisms and all endomorphisms of an undirected cycle graph <jats:italic>C<jats:sub>n<\/jats:sub>\n                  <\/jats:italic> with <jats:italic>n<\/jats:italic> vertices. We also describe Green\u2019s relations and regularity of these monoids and calculate their cardinalities.<\/jats:p>","DOI":"10.1515\/ms-2024-0078","type":"journal-article","created":{"date-parts":[[2024,10,15]],"date-time":"2024-10-15T07:45:46Z","timestamp":1728978346000},"page":"1071-1088","source":"Crossref","is-referenced-by-count":3,"title":["On monoids of endomorphisms of a cycle graph"],"prefix":"10.1515","volume":"74","author":[{"given":"Ilinka","family":"Dimitrova","sequence":"first","affiliation":[{"name":"Department of Mathematics Faculty of Mathematics and Natural Science South-West University \u201dNeofit Rilski\u201d 2700 Blagoevgrad Bulgaria"}]},{"given":"Vitor H.","family":"Fernandes","sequence":"additional","affiliation":[{"name":"Center for Mathematics and Applications (NOVA Math) and Department of Mathematics Faculdade de Ci\u00eancias e Tecnologia Universidade Nova de Lisboa Monte da Caparica 2829-516 Caparica Portugal"}]},{"given":"J\u00f6rg","family":"Koppitz","sequence":"additional","affiliation":[{"name":"Institute of Mathematics and Informatics Bulgarian Academy of Sciences 1113 Sofia Bulgaria"}]},{"given":"Teresa M.","family":"Quinteiro","sequence":"additional","affiliation":[{"name":"Center for Mathematics and Applications (NOVA Math) and Department of Mathematics Faculdade de Ci\u00eancias e Tecnologia Universidade Nova de Lisboa Monte da Caparica 2829-516 Caparica Portugal"},{"name":"Department of Mathematics Instituto Superior de Engenharia de Lisboa R. 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