{"title":"Orientably-regular embeddings of complete multigraphs","authors":"Štefan Gyürki, Soňa Pavlíková, Jozef Širáň","doi":"10.1016/j.jctb.2024.11.004","DOIUrl":null,"url":null,"abstract":"<div><div>An embedding of a graph on an orientable surface is <em>orientably-regular</em> (or <em>rotary</em>, in an equivalent terminology) if the group of orientation-preserving automorphisms of the embedding is transitive (and hence regular) on incident vertex-edge pairs of the graph. A classification of orientably-regular embeddings of complete graphs was obtained by L.D. James and G.A. Jones (1985) <span><span>[10]</span></span>, pointing out interesting connections to finite fields and Frobenius groups. By a combination of graph-theoretic methods and tools from combinatorial group theory we extend results of James and Jones to classification of orientably-regular embeddings of complete multigraphs with arbitrary edge-multiplicity.</div></div>","PeriodicalId":54865,"journal":{"name":"Journal of Combinatorial Theory Series B","volume":"171 ","pages":"Pages 71-95"},"PeriodicalIF":1.2000,"publicationDate":"2024-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Combinatorial Theory Series B","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0095895624000959","RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
An embedding of a graph on an orientable surface is orientably-regular (or rotary, in an equivalent terminology) if the group of orientation-preserving automorphisms of the embedding is transitive (and hence regular) on incident vertex-edge pairs of the graph. A classification of orientably-regular embeddings of complete graphs was obtained by L.D. James and G.A. Jones (1985) [10], pointing out interesting connections to finite fields and Frobenius groups. By a combination of graph-theoretic methods and tools from combinatorial group theory we extend results of James and Jones to classification of orientably-regular embeddings of complete multigraphs with arbitrary edge-multiplicity.
期刊介绍:
The Journal of Combinatorial Theory publishes original mathematical research dealing with theoretical and physical aspects of the study of finite and discrete structures in all branches of science. Series B is concerned primarily with graph theory and matroid theory and is a valuable tool for mathematicians and computer scientists.