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A formula for eigenvalues of integral Cayley graphs over abelian groups (2411.06386v1)
Published 10 Nov 2024 in math.CO
Abstract: Let $Z$ be an abelian group, $ x \in Z$, and $[x] = { y : \langle x \rangle = \langle y \rangle }$. 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]$. This formula involves an analogue of M$\ddot{\text{o}}$bius function.