Integral cayley graphs over semi-dihedral groups

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2021-01-01 DOI:10.2298/AADM190330001C

Tao Cheng, Lihua Feng, Guihai Yu, Chi Zhang

引用次数: 3

Abstract

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 | a4n = b2 = 1; bab = a2n-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 hai. 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.

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半二面体群上的积分cayley图

积分图的分类是Harary和Schwenk在1974年提出的一个难题。本文利用特征表处理了半二面体群SD8n = ?a,b | a4n = b2 = 1上的Cayley图的相应问题;b = a2n-1?n ?2. 本文给出了SD8n上Cayley图的完整性的几个充分必要条件，并利用hai的布尔代数得到了SD8n上Cayley图完整性的几个简单充分条件。特别地，我们给出了一素数p在半二面体群SD2n (n?4)和SD8p上的Cayley图的完整性的充分条件，由此确定了SD2n和SD8p上的无限类的积分Cayley图。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.