<?xml version="1.0" encoding="UTF-8"?><xml><records><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Dimitrova, I.</style></author><author><style face="normal" font="default" size="100%">Fernandes, Vítor H.</style></author><author><style face="normal" font="default" size="100%">Koppitz, J.</style></author><author><style face="normal" font="default" size="100%">T.M. Quinteiro</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">On monoids of endomorphisms of a cycle graph</style></title><secondary-title><style face="normal" font="default" size="100%">Mathematica Slovaca (DOI 10.1515/ms-2024-0078; Online 15 October 2024)</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2024</style></year></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://www.degruyter.com/document/doi/10.1515/ms-2024-0078/html</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">74</style></volume><pages><style face="normal" font="default" size="100%">1071-1088</style></pages><abstract><style face="normal" font="default" size="100%">&lt;p&gt;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 $wEnd(C_n)$ and $End(C_n)$ of all weak endomorphisms and all endomorphisms of an undirected cycle graph $C_n$ with $n$ vertices. We also describe Green's relations and regularity of these monoids and calculate their cardinalities.&lt;/p&gt;
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