On ve-degree molecular topological properties of silicate and oxygen networks

Abstract

Silicate based inorganic materials are important for the synthesis of a new inorganic molecules in which the studies for ultrahigh proton conductivity and catalysis. Quantitative structure-property and structureactivity relationships of the silicate oxygen networks necessitate expressions for the molecular topological features of these networks. In QSPR/QSAR studies, physicochemical characteristics and molecular topological indices such as atom-bond connectivity (ABC), geometric-arithmetic (GA), harmonic (H) and sum-connectivity (χ) indices are used to model the physicochemical properties of chemical compounds and networks. These topological indices are based on the degrees of the vertices (atoms) of a connected graph. Recently, two novel degree concepts have been defined in graph theory; ev-degrees and ve-degrees. In this study by using the ve-degree concept, we define ve-degree atom-bond connectivity (ve-ABC), ve-degree geometric-arithmetic (ve-GA), ve-degree harmonic (ve-H) and ve-degree sum-connectivity (ve-χ) indices as parallel to their corresponding classical degree versions. We show that the ve-degree sum-connectivity index give better correlation than Wiener, Zagreb and Randić indices to predict the acentric factor of octanes. Also, we compute the ve-degree topological indices for some silicate oxygen netwoks such as dominating oxide network (DOX), regular triangulene oxide network (RTOX), dominating silicate network (DSL) and derive analytical closed formulae of these networks.

Two New Arithmetic-Geometric ve-degree Indices

“…The molecular structure of a dominating oxide network is presented in Figure 1. In [8], Ediz obtained the partition of the edges with respect to their sum degree of end vertices of dominating oxide networks in Table 1.…”

“…Recently, Ediz [8] defined the ve-degree geometric-arithmetic index of a connected graph G and it is defined as…”

“…We consider the families of dominating oxide networks and regular triangulate oxide networks [8]. In this paper, the arithmetic-geometric ve-degree index and multiplicative arithmetic-geometric ve-degree index of dominating oxide networks and regular triangulate oxide networks are determined.…”

On Harmonic and Ev-Degree Molecular Topological Properties of DOX, RTOX and DSL Networks

“…On mathematical properties of these novel concepts we referred the interested reader to the reference [Horoldagva, Das, Selenge (2019)]. Ev-degree and Ve-degree Zagreb indices and Ev-degree and Ve-degree Randic indices have been defined by using ve-degree concept in Ediz et al [Ediz (2017a, 2017b; Şahin and Ediz (2018)]. The prediction power of the ve-degree Zagreb indices is stronger than the classical Zagreb indices.…”

On ve-degree Indices and their Polynomials of Dominating Oxide Networks

“…We consider the family of dominating oxide networks [26,27]. In this paper, we determine the first and second ve-degree indices, the first and second hyper-ve-degree indices, the third ve-degree index for dominating oxide networks.…”