Topological indices of total graph of the ring Z? × Zm

Abstract

In this paper, we compute some distance-based topological indices namely Wiener index, hyper Wiener index and reverse Wiener index of the total graph of the ring Zn × Zm. We also compute some eccentricity-based topological indices namely first Zagreb eccentricity index, second Zagreb eccentricity index, eccentric connectivity index, connective eccentricity index and eccentric distance sum index of the total graph of the ring Zn × Zm. Finally, we compute some degree-based topological indices namely second Zagreb index, product-connectivity index, sum connectivity index, atom-bond connectivity index and geometric arithmetic index of the total graph of the ring Zn ×Zm when both n and m are even, when n or m is even, and the case when n and m are both prime numbers (not neccesarily distinct).