On integral Cayley sum graphs

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• 作者：Marzieh Amooshahi ; Bijan Taeri
• 关键词：Cayley sum graph ; integral graph ; Cayley sum integral group
• 刊名：Indian Journal of Pure and Applied Mathematics
• 出版年：2016
• 出版时间：December 2016
• 年：2016
• 卷：47
• 期：4
• 页码：583-601
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics, general; Applications of Mathematics; Numerical Analysis;
• 出版者：Indian National Science Academy
• ISSN：0975-7465
• 卷排序：47

文摘

Let S be a subset of a finite abelian group G. The Cayley sum graph Cay+(G, S) of G with respect to S is a graph whose vertex set is G and two vertices g and h are joined by an edge if and only if g + h ∈ S. We call a finite abelian group G a Cayley sum integral group if for every subset S of G, Cay+(G, S) is integral i.e., all eigenvalues of its adjacency matrix are integers. In this paper, we prove that all Cayley sum integral groups are represented by Z₃ and Zn₂n, n ≥ 1, where Z_k is the group of integers modulo k. Also, we classify simple connected cubic integral Cayley sum graphs.