INTEGRAL CAYLEY GRAPHS OVER SEMI-DIHEDRAL GROUPS

被引：6

作者：

Cheng, Tao ^{[1
]}

Feng, Lihua ^{[2
]}

Yu, Guihai ^{[3
]}

Zhang, Chi ^{[4
]}

机构：

[1] Shandong Normal Univ, Sch Math & Stat, Jinan 250014, Shandong, Peoples R China

[2] Cent South Univ, Sch Math & Stat, New Campus, Changsha 410083, Hunan, Peoples R China

[3] Guizhou Univ Finance & Econ, Coll Big Data Stat, Guiyang 550025, Guizhou, Peoples R China

[4] Northeastern Univ, Coll Sci, Dept Math, Shenyang 110819, Liaoning, Peoples R China

来源：

APPLICABLE ANALYSIS AND DISCRETE MATHEMATICS | 2023年 / 17卷 / 02期

基金：

中国国家自然科学基金;

关键词：

Integral Cayley graph; Eigenvalue; Character; Semi-dihedral groups; TREES;

D O I：

10.2298/AADM190330001C

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Classifying integral graphs is a hard problem that initiated by Harary and Schwenk in 1974. In this paper, with the help of character table, we treat the corresponding problem for Cayley graphs over the semi-dihedral group SD8n= < a, b vertical bar a(4n) = b(2) = 1, bab = a(2n-1)>, n >= 2. We present several necessary and sufficient conditions for the integrality of Cayley graphs over SD8n, we also obtain some simple sufficient conditions for the integrality of Cayley graphs over SD8n in terms of the Boolean algebra of < a >. In particular, we give the sufficient conditions for the integrality of Cayley graphs over semi-dihedral groups SD2n (n >= 4) and SD8p for a prime p, from which we determine several infinite classes of integral Cayley graphs over SD2n and SD8p.

引用

页码：334 / 356

页数：23

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