{"title":"Generalized Cayley maps and their Petrie duals","authors":"Robert Jajcay, Jozef Širáň, Yan Wang","doi":"10.26493/1855-3974.2408.42e","DOIUrl":null,"url":null,"abstract":"Cayley maps are embeddings of Cayley graphs in orientable surfaces which possess a group of orientation preserving automorphisms acting regularly on the vertices. We generalize the concept of a Cayley map by considering embeddings of Cayley graphs in both orientable and non-orientable surfaces and by requiring a group of automorphisms acting regularly on vertices that does not have to consist entirely of orientation preserving automorphisms. This leads to new families of maps in both the orientable and non-orientable cases. Since the Petrie dual operator preserves the property of being a generalized Cayley map, throughout the paper we consider the action of this operator on our maps.","PeriodicalId":49239,"journal":{"name":"Ars Mathematica Contemporanea","volume":"20 1","pages":"0"},"PeriodicalIF":0.6000,"publicationDate":"2023-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Ars Mathematica Contemporanea","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.26493/1855-3974.2408.42e","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
Cayley maps are embeddings of Cayley graphs in orientable surfaces which possess a group of orientation preserving automorphisms acting regularly on the vertices. We generalize the concept of a Cayley map by considering embeddings of Cayley graphs in both orientable and non-orientable surfaces and by requiring a group of automorphisms acting regularly on vertices that does not have to consist entirely of orientation preserving automorphisms. This leads to new families of maps in both the orientable and non-orientable cases. Since the Petrie dual operator preserves the property of being a generalized Cayley map, throughout the paper we consider the action of this operator on our maps.
期刊介绍:
Ars mathematica contemporanea will publish high-quality articles in contemporary mathematics that arise from the discrete and concrete mathematics paradigm. It will favor themes that combine at least two different fields of mathematics. In particular, we welcome papers intersecting discrete mathematics with other branches of mathematics, such as algebra, geometry, topology, theoretical computer science, and combinatorics. The name of the journal was chosen carefully. Symmetry is certainly a theme that is quite welcome to the journal, as it is through symmetry that mathematics comes closest to art.