{"title":"Distance-regular Cayley graphs over (pseudo-) semi-dihedral groups","authors":"Xueyi Huang , Lu Lu , Xiongfeng Zhan","doi":"10.1016/j.dam.2025.04.006","DOIUrl":null,"url":null,"abstract":"<div><div>Distance-regular graphs constitute an important class of regular graphs exhibiting remarkable combinatorial symmetry. In 2007, Miklavič and Potočnik initiated the systematic study of distance-regular Cayley graphs, extending the classical problem of characterizing strongly regular Cayley graphs (equivalent to investigating regular partial difference sets). In this paper, we provide a partial characterization of distance-regular Cayley graphs over semi-dihedral groups and pseudo-semi-dihedral groups, both of which are 2-groups that contain a cyclic subgroup of index 2.</div></div>","PeriodicalId":50573,"journal":{"name":"Discrete Applied Mathematics","volume":"372 ","pages":"Pages 95-108"},"PeriodicalIF":1.0000,"publicationDate":"2025-04-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Discrete Applied Mathematics","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0166218X25001787","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
Distance-regular graphs constitute an important class of regular graphs exhibiting remarkable combinatorial symmetry. In 2007, Miklavič and Potočnik initiated the systematic study of distance-regular Cayley graphs, extending the classical problem of characterizing strongly regular Cayley graphs (equivalent to investigating regular partial difference sets). In this paper, we provide a partial characterization of distance-regular Cayley graphs over semi-dihedral groups and pseudo-semi-dihedral groups, both of which are 2-groups that contain a cyclic subgroup of index 2.
期刊介绍：
The aim of Discrete Applied Mathematics is to bring together research papers in different areas of algorithmic and applicable discrete mathematics as well as applications of combinatorial mathematics to informatics and various areas of science and technology. Contributions presented to the journal can be research papers, short notes, surveys, and possibly research problems. The "Communications" section will be devoted to the fastest possible publication of recent research results that are checked and recommended for publication by a member of the Editorial Board. The journal will also publish a limited number of book announcements as well as proceedings of conferences. These proceedings will be fully refereed and adhere to the normal standards of the journal.
Potential authors are advised to view the journal and the open calls-for-papers of special issues before submitting their manuscripts. Only high-quality, original work that is within the scope of the journal or the targeted special issue will be considered.
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