On the normalized Laplacian spectrum of the comaximal graphs

Let R be a commutative ring with nonzero identity. The comaximal graph of R, denoted by G(R), is a simple graph with vertex set R, and two distinct vertices a and b are adjacent if and only if Ra + Rb = R. Let Gamma(2)(R) be an induced subgraph of Gamma(R) with nonunit elements of R as vertices. In this paper, we describe the normalized Laplacian spectrum of Gamma(Z(n)), and we determine it for some values of n, where Z(n) is the ring of integers modulo n. Moreover, we investigate the normalized Laplacian energy and general Randic index of Gamma(2)(Z(n)).