<?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%">Fernandes, Vítor H.</style></author><author><style face="normal" font="default" size="100%">Paulista, Tânia</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">On the monoid of partial isometries of a cycle graph</style></title><secondary-title><style face="normal" font="default" size="100%">Turkish Journal of Mathematics (DOI 10.55730/1300-0098.3460)</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2023</style></year></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://journals.tubitak.gov.tr/math/vol47/iss6/10/</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">47</style></volume><pages><style face="normal" font="default" size="100%">1746-1760</style></pages><abstract><style face="normal" font="default" size="100%">&lt;p&gt;In this paper we consider the monoid DPC_n of all partial isometries of a n-cycle graph C_n. We show that DPC_n is the submonoid of the monoid of all oriented partial permutations on a n-chain whose elements are precisely all restrictions of a dihedral group of order 2n. Our main aim is to exhibit a presentation of DPC_n. We also describe Green's relations of DPC_n and calculate its cardinality and rank. &lt;/p&gt;
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