Integral equienergetic non-isospectral unitary Cayley graphs

We prove that the Cayley graphs $X(G,S)$ and $X^+(G,S)$ are equienergetic for any abelian group $G$ symmetric subset $S$. then focus on family of unitary $G_R=X(R,R^*)$, where $R$ is a finite commutative ring with identity. show under mild conditions, $\{G_R, G_R^+\}$ pairs integral non-isospectral (generically connected non-bipartite). Then, we obtain conditions such \bar G_R\}$ graphs. Finally, characterize all triples G_R^+, G_R \}$ also Ramanujan.