Topological index analysis of a class of networks analogous to alicyclic hydrocarbons and their derivatives

Abstract

Alicyclic hydrocarbons and their derivatives have been studied extensively by researchers in recent years. Actually, they are a subclass of the toroidal networks. The kind of networks can be characterized as the toroidal networks obtained from associating lots of identical basic sub-networks into a cycle. In this paper, we study topological indices correlated with the toroidal networks, such as resistance distance, the Kirchhoff index, and the degree-Kirchhoff index by creating n-separations which can compute resistance distance simply. Furthermore, we also derive and analyze lots of topological indices based on degree of the toroidal networks. For instance, the Zagreb index, the general Randić index, the Forgotten index, and so on. These characteristic quantities can be utilized to evaluate the properties of alicyclic hydrocarbons as well as can be extensively applied to many fields, like mathematics, physics, chemistry, biology, or other fields.