文献类型：期刊文献

英文题名：Fourier Analysis on Distance-Regular Cayley Graphs over Abelian Groups

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

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

年份：2026

卷号：33

期号：1

外文期刊名：ELECTRONIC JOURNAL OF COMBINATORICS

收录：;WOS:【SCI-EXPANDED(收录号:WOS:001673227600001)】；

基金：Acknowledgements The authors would like to thank Professor S tefko Miklavic and the anonymous reviewers for their valuable comments and helpful suggestions. X. Huang was supported by the National Natural Science Foundation of China (No. 12471324) and the Natural Science Foundation of Shanghai (No. 24ZR1415500) . L. Lu was supported by the National Natural Science Foundation of China (No. 12371362) and the Natural Science Foundation of Hunan Province (No. 2021JJ40707) . X. Zhan was supported by the Student Innovation and Entrepreneurship Training Program (No. S202510251167) .

语种：英文

摘要：The problem of constructing or characterizing strongly regular Cayley graphs (or equivalently, regular partial difference sets) has garnered significant attention over the past half-century. A classic result in this area is the complete classification of strongly regular Cayley graphs over cyclic groups, which was established by Bridges and Mena (1979), independently by Ma (1984), and partially by Marusic (1989). Miklavic and Potocnik (2003) extended this work by providing a complete characterization of distance-regular Cayley graphs over cyclic groups through the method of Schur rings. Building on this, Miklavic and Potocnik (2007) formally posed the problem of characterizing distance-regular Cayley graphs for arbitrary classes of groups. Within this framework, abelian groups are of particular significance, as many distance-regular graphs with classical parameters are Cayley graphs over abelian groups. In this paper, we employ Fourier analysis on abelian groups to establish connections between distance-regular Cayley graphs over abelian groups and combinatorial objects in finite geometry. By combining these insights with classical results from finite geometry, we classify all distance-regular Cayley graphs over the group Zn circle plus Zp, where n is a positive integer and p is an odd prime.