文献类型：期刊文献

英文题名：Splitting fields of mixed Cayley graphs over abelian groups

作者：Huang, Xueyi[1];Lu, Lu[2];Moenius, Katja[3]

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;[3]Wurzburg Univ, Dept Math, Emil Fischer Str 40, D-97074 Wurzburg, Germany

年份：2023

卷号：58

期号：3

起止页码：681

外文期刊名：JOURNAL OF ALGEBRAIC COMBINATORICS

收录：;WOS:【SCI-EXPANDED(收录号:WOS:001068135700001)】；

基金：The authors are so grateful to the referee for their valuable comments and corrections which improve the presentation of the paper. L. Lu is supported by National Natural Science Foundation of China (Grant No. 12001544) and Natural Science Foundation of Hunan Province (Grant No. 2021JJ40707). X. Huang is supported by National Natural Science Foundation of China (Grant No. 11901540).

语种：英文

外文关键词：Mixed Cayley graph; Integral graph; Splitting Field; Algebraic degree

摘要：The splitting field SF(Gamma) of a mixed graph Gamma is the smallest field extension of Q which contains all eigenvalues of the Hermitian adjacency matrix of Gamma. The extension degree [SF(Gamma) : Q] is called the algebraic degree of Gamma. In this paper, we determine the splitting fields and algebraic degrees of mixed Cayley graphs over abelian groups. This generalizes the main results of Monius (J Algebra 594(15):154-169, 2022). Additionally, we provide a characterization of integralmixed Cayley graphs over abelian groups, which implies the main result of Kadyan and Bhattacharjya (Electron J Combin 28(4):P4.46, 2021).