Metric-Based Resolvability of Quartz Structure

Chinu Singla,Badria Sulaiman Alfurhood,Yash Singh Pathania,Manar Ahmed Hamza,Mohammed Rizwanullah,Mohammad Mahzari,Anwer Mustafa Hilal,Fahd N Al-Wesabi

doi:10.32604/cmc.2022.022064

Abstract

Silica has three major varieties of crystalline. Quartz is the main and abundant ingredient in the crust of our earth. While other varieties are formed by the heating of quartz. Silica quartz is a rich chemical structure containing enormous properties. Any chemical network or structure can be transformed into a graph, where atoms become vertices and the bonds are converted to edges, between vertices. This makes a complex network easy to visualize to work on it. There are many concepts to work on chemical structures in terms of graph theory but the resolvability parameters of a graph are quite advance and applicable topic. Resolvability parameters of a graph is a way to getting a graph into unique form, like each vertex or edge has a unique identification by means of some selected vertices, which depends on the distance of vertices and its pattern in a particular graph. We have dealt some resolvability parameters of quartz. We computed the resolving set for quartz structure and its variants, wherein we proved that all the variants of resolvability parameters of quartz structures are constant and do not depend on the order of the graph.

Highlights

Molecular graph is a simple graph transformed from a chemical network or a structure
We found the exact metric, edge metric, fault-tolerant metric, fault-tolerant edge metric dimension and bounds of partition dimension of silica quartz which is denoted as Qk throughout the research work
Results on the Resolvability of SiO2 Quartz (Qk) we will reshape the structure of quartz (Qk) determining the different resolvability parameters

Summary

Introduction

Molecular graph is a simple graph transformed from a chemical network or a structure. Definition 1.2: The main role in all the resolvability parameters is known as either location, position or representations and formally denoted by r(α|L) for the vertex α and L is the subset of selected vertices from the vertex set. Assuming a subset of selected vertices Le, if the position r(e|Le) of each e is unique of a graph Le is called as edge metric resolving set and dime(p) is the minimum count of members of Le, called as edge metric dimension.

Results

Conclusion