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.
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Amooshahi, M., Taeri, B. On integral Cayley sum graphs. Indian J Pure Appl Math 47, 583–601 (2016). https://doi.org/10.1007/s13226-016-0204-5
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DOI: https://doi.org/10.1007/s13226-016-0204-5