文献类型：期刊文献

英文题名：Distance-regular Cayley graphs over Zps ⊕ Zp

作者：Zhan, Xiongfeng[1];Lu, Lu[2];Huang, Xueyi[1]

机构：[1]East China Univ Sci & Technol, Sch Math, Shanghai 200237, Peoples R China;[2]Cent South Univ, Sch Math & Stat, Changsha 410083, Hunan, Peoples R China

年份：2025

卷号：25

期号：1

外文期刊名：ARS MATHEMATICA CONTEMPORANEA

收录：;WOS:【SCI-EXPANDED(收录号:WOS:001429352500008)】；

基金：The authors would like to thank the anonymous referees for their remarks and corrections, which have enabled us to greatly improve the paper. dagger The author is supported by National Natural Science Foundation of China (Grant Nos. 12371362, 12001544) and Natural Science Foundation of Hunan Province (Grant No. 2021JJ40707) . double dagger Corresponding author. The author is supported by National Natural Science Foundation of China (Grant No. 12471324) and Natural Science Foundation of Shanghai (Grant No. 24ZR1415500) .

语种：英文

外文关键词：Distance-regular graph; Cayley graph; Schur ring; Fourier transformation; transversaldesign

摘要：In 2007, Miklavic and Potocnik proposed the problem of characterizing distance-regular Cayley graphs, which can be viewed as an extension of the problem of identifying strongly regular Cayley graphs, or equivalently, regular partial difference sets. Let p be an odd prime. In this paper, all distance-regular Cayley graphs over Z(p)s circle plus Z(p ) are identified. It is shown that every such graph is isomorphic to a complete graph, a complete multipartite graph, or the line graph of a transversal design TD(r, p) with 2 < r < p - 1.