Edge Metric and Fault-Tolerant Edge Metric Dimension of Hollow Coronoid

Ali N A Koam,Ali Ahmad,Muhammad Ibrahim,Muhammad Azeem

doi:10.3390/math9121405

Ali N A Koam, Ali Ahmad + Show 2 more

Open Access

https://doi.org/10.3390/math9121405

Copy DOI

Abstract

Geometric arrangements of hexagons into six sides of benzenoids are known as coronoid systems. They are organic chemical structures by definition. Hollow coronoids are divided into two types: primitive and catacondensed coronoids. Polycyclic conjugated hydrocarbon is another name for them. Chemical mathematics piques the curiosity of scientists from a variety of disciplines. Graph theory has always played an important role in making chemical structures intelligible and useful. After converting a chemical structure into a graph, many theoretical and investigative studies on structures can be carried out. Among the different parameters of graph theory, the dimension of edge metric is the most recent, unique, and important parameter. Few proposed vertices are picked in this notion, such as all graph edges have unique locations or identifications. Different (edge) metric-based concept for the structure of hollow coronoid were discussed in this study.

Highlights

Molecular graph theory is considered a diversified area of chemistry and mathematics, as it deals with application of mathematics for chemical structures
There are a variety of approaches to evaluate and research electrical circuits using graph theory, and graph theoretical parameters may be used in electronics
In 1975, Slater [2,3], presented an effective notion of network visualization known as metric basis or resolving set, in which principle nodes were picked to achieve the whole set of vertices in a unique identity in terms of distance positions

Summary

Introduction

Molecular graph theory is considered a diversified area of chemistry and mathematics, as it deals with application of mathematics for chemical structures. The above notions are renowned resolvability parameters in terms of metric that have been researched for many graphs, networks, and structures. Suppose א(V (א), E(א)) is an undirected graph of a chemical structure (network) with V (א) is called as set of principal nodes (vertex set) and E(א) is the set of branches (edge set).

Results

Conclusion