Spectral properties of Cayley graphs over finite commutative rings

Let R be a finite commutative ring with unity and x be a non-zero element of R. In this paper, we calculate the spectrum and energy of the Cayley graph Cay(R,xR*), and also compute the energy of their compliment graph. It generalizes to Theorem 2.4 and Theorem 4.1 of https://doi.org/10.1016/j.laa.2011.03.015. Further, we characterize the commutative ring R such that the Cayley graph Cay(R,xR*) is Ramanujan. This generalizes to Theorem 12 of https://doi.org/10.48550/arXiv.1205.5932.