Topological indices of the mk-graph

Abstract

This paper is devoted to the study of a new graph, called $m^k$-graph and denoted by $m^k\left(G\right)$, that arises from a simple graph G by k successive iterations of a special kind of construction. We provide some of its topological indices such as Wiener index, Hyper-Wiener index, Wiener polarity, Zagreb indices, Schultz and modified Schultz indices and Wiener-type invariant. Some Formulas concerning classical graphs are settled to show the scope of this study.