A formula for eigenvalues of integral Cayley graphs over abelian groups

2024/11/10 by Priya, Kadyan, Monu · 1 citation
#05C50 #20C15 #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2411.06386

Abstract

Let Z be an abelian group, x ∈ Z, and [x] = \ y : ⟨ x ⟩ = ⟨ y ⟩ \. A graph is called integral if all its eigenvalues are integers. It is known that a Cayley graph is integral if and only if its connection set can be express as union of the sets [x] . In this paper, we determine an algebraic formula for eigenvalues of the integral Cayley graph when the connection set is [x]. This formula involves an analogue of Mobius function.

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