{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,25]],"date-time":"2025-09-25T18:06:14Z","timestamp":1758823574981,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>The Cayley Isomorphism property for combinatorial objects was introduced by L. Babai in 1977. Since then it has been intensively studied for binary relational structures: graphs, digraphs, colored graphs etc. In this paper we study this property for oriented Cayley maps.\u00a0A Cayley map is a Cayley graph provided by\u00a0a cyclic rotation of its connection set. \u00a0If the underlying graph is connected, then the map is an embedding of a Cayley graph into an oriented surface with the same cyclic rotation around every vertex.Two Cayley maps are called Cayley isomorphic if there exists a map isomorphism between them which is a group isomorphism too. We say that a finite group $H$ is a CIM-group\u00a0if any two Cayley maps over $H$ are isomorphic if and only if they are Cayley isomorphic.The paper contains two main results regarding CIM-groups. The first one provides necessary conditons for being a CIM-group. It shows that a CIM-group should be one of the following$$\\mathbb{Z}_m\\times\\mathbb{Z}_2^r, \\\\mathbb{Z}_m\\times\\mathbb{Z}_{4},\\\\mathbb{Z}_m\\times\\mathbb{Z}_{8}, \\ \\mathbb{Z}_m\\times Q_8, \\\\mathbb{Z}_m\\rtimes\\mathbb{Z}_{2^e}, e=1,2,3,$$\u00a0where $m$ is an odd square-free number and $r$ a non-negative integer. Our second main result shows that the groups $\\mathbb{Z}_m\\times\\mathbb{Z}_2^r$, $\\mathbb{Z}_m\\times\\mathbb{Z}_{4}$, $\\mathbb{Z}_m\\times Q_8$\u00a0contained in the above list\u00a0are indeed CIM-groups.<\/jats:p>","DOI":"10.37236\/5962","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T15:37:31Z","timestamp":1578670651000},"source":"Crossref","is-referenced-by-count":1,"title":["The Cayley Isomorphism Property for Cayley Maps"],"prefix":"10.37236","volume":"25","author":[{"given":"Mikhail","family":"Muzychuk","sequence":"first","affiliation":[]},{"given":"G\u00e1bor","family":"Somlai","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2018,3,2]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v25i1p42\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v25i1p42\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T04:38:14Z","timestamp":1579235894000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v25i1p42"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,3,2]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2018,1,12]]}},"URL":"https:\/\/doi.org\/10.37236\/5962","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2018,3,2]]},"article-number":"P1.42"}}