Energy and Wiener index of Total Graph over Ring Zn

Let Zn be a commutative ring with Z(Zn) its set of zero-divisors. In this paper, we study the total graph of Zn, denoted by T(Γ(Zn)). It is the (undirected) graph with all elements of Zn as vertices, and for distinct x,y∈Zn, the vertices x and y are adjacent if and only if x+y∈Z(Zn). We study the Energy, Laplacian matrix, Laplacian energy, Distance energy and Wiener index of the total graph of Zn, where n is the product of primes. We also find the relation among all energies. Moreover, we have given MATLAB coding of our calculations for Energy and Wiener index.