On Cayley Sum Graphs of Non-Abelian Groups

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• 作者：Marzieh Amooshahi ; Bijan Taeri
• 关键词：Cayley sum graph ; Integral graph ; Integral Cayley sum graph ; 05C25 ; 05C50 ; 15A18
• 刊名：Graphs and Combinatorics
• 出版年：2016
• 出版时间：January 2016
• 年：2016
• 卷：32
• 期：1
• 页码：17-29
• 全文大小：481 KB
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• 作者单位：Marzieh Amooshahi (1)
  Bijan Taeri (1)
  
  1. Department of Mathematical Sciences, Isfahan University of Technology, 84156-83111, Isfahan, Iran
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Combinatorics
  Engineering Design
  
• 出版者：Springer Japan
• ISSN：1435-5914

文摘

Let \(G\) be a finite group and \(S\) be a square-free normal subset of \(G\). The Cayley sum graph \(\mathrm{Cay}^+(G, S)\) of \(G\) with respect to \(S\) is a simple graph whose vertex set is \(G\) and two vertices \(g\) and \(h\) are joined by an edge if and only if \(g h \in S\). In this paper, we obtain necessary and sufficient conditions on \(S\) such that \(\mathrm{Cay}^+(G, S)\) is connected. Also, we prove that if \(G\) is a non-abelian group and \(|S|=3\), then \(\mathrm{Cay}^+(G, S)\) is a connected integral graph if and only if \(G\) is isomorphic to \(S_3\), the symmetric group on \(3\) letters. Keywords Cayley sum graph Integral graph Integral Cayley sum graph