On integral Cayley sum graphs

Marzieh Amooshahi () and Bijan Taeri ()
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Marzieh Amooshahi: Isfahan University of Technology
Bijan Taeri: Isfahan University of Technology

Indian Journal of Pure and Applied Mathematics, 2016, vol. 47, issue 4, 583-601

Abstract: Abstract 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 Zn2 n, n ≥ 1, where Zk is the group of integers modulo k. Also, we classify simple connected cubic integral Cayley sum graphs.

Keywords: Cayley sum graph; integral graph; Cayley sum integral group (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1007/s13226-016-0204-5

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