Studying the structure of some networks using certain topological indices

Abstract

Analyzing the structural properties of graphs, networks and particularly complex networks is a research topic with ongoing interest. One of the approaches in studying structural properties is finding quantitative measures that encode structural information of the entire network by a real number. Recently, a number of graph invariants, also known as topological indices, have been used as measures to analyze the whole structure of networks. In this paper, we study a class of large networks named Equilateral Tetra Sheet network ETTSn and Hex derived network HDNn. We give the construction method for these networks and extract its structural properties. Then, we employ a computational technique called edge-cut method to obtain new analytical expressions for certain topological indices, such as, the Wiener index (W) and the generalized Terminal Wiener index (TWK with K={δ,Δ}). After that, we compare the efficiency of the computed indices by using graphical representations. At the end, we summarize our findings.