On Some New Neighborhood Degree-Based Indices for Some Oxide and Silicate Networks

Sourav Mondal,Anita Pal,Nilanjan De

doi:10.3390/j2030026

Abstract

Topological indices are numeric quantities that describes the topology of molecular structure in mathematical chemistry. An important area of applied mathematics is the chemical reaction network theory. Real-world problems can be modeled using this theory. Due to its worldwide applications, chemical networks have attracted researchers since their foundation. In this report, some silicate and oxide networks are studied, and exact expressions of some newly-developed neighborhood degree-based topological indices named as the neighborhood Zagreb index ( M N ), the neighborhood version of the forgotten topological index ( F N ), the modified neighborhood version of the forgotten topological index ( F N ∗ ), the neighborhood version of the second Zagreb index ( M 2 ∗ ), and neighborhood version of the hyper Zagreb index ( H M N ) are obtained for the aforementioned networks. In addition, a comparison among all the indices is shown graphically.

Highlights

Networks connect nodes that are somehow interconnected
In most frequently-found silicates, including almost all silicate minerals found in the crust of the Earth, each silicon atom comprises the center of a tetrahedron (Figure 1), the corners of which are occupied by oxygen atoms, connected to it by single covalent bonds according to the octet rule
Silicate networks are built by different silicate structures

Summary

Introduction

Networks connect nodes that are somehow interconnected. Numerous personal computers connected together form a network. Inspired by the works [6,7,8], we designed some new degree-based topological indices [9,10] having nice correlations with entropy and the acentric factor In [22], topological indices for the copper (II) oxide network were obtained. For further work related to this field, readers are referred to [23,24,25,26] Motivated by those works, in this paper, we obtain some exact expressions of five novel indices described above for some silicate and oxide networks and compare the results graphically. We conclude this report with a comparative study of the indices for different networks under consideration

Motivation

Computation of Topological Indices

Remarks and Conclusions