Hosoya, Schultz and modified Schultz polynomials and their topological indices of prime graphs of commutative ring Zn

A Hosoya polynomial of any graph is defined by Sigma(u)(,v is an element of V) ((G)) x(d) (u, v), while Schultz and modified Schultz polynomials of a gvreavphC ) are defined as Sc = Sigma(u)(,v is an element of V) ((G)) (deg(u) + deg(v))x(d(u,v)) and S*c = Sigma(u)(,v is an element of V) ((G)) (deg(u)deg(v))x(d(u,v)), respectively. Moreover, Wiener, Harary, Schultz and modified Schultz indices are related. In this pa- per, we investigate and compute new formulas of these polynomials and their prime graph indices of commutative ring Z(n).