On Computation and Analysis of Topological Index-Based Invariants for Complex Coronoid Systems

Muhammad Aamer Rashid,Sarfraz Ahmad,Mohammed K A Kaabar,Muhammad Kamran Siddiqui,Miaomiao Wang

doi:10.1155/2021/4646501

Abstract

In chemical graph theory, benzenoid systems are interrogated as they exhibit the chemical compounds known as benzenoid hydrocarbons. Benzenoid schemes are circumscribed as planar connected finite graphs having no cut vertices wherein the entire internal sections are collaboratively congruent regular hexagon. The past couple of decennium has acknowledged an extravagant development regarding implementation of information theoretic framework in miscellaneous ramification of science, for instance, in social sciences, biological, physical, and engineering. Explicitly, this tremendous improvement has been outstanding in the field of soft computing, molecular biology, and information technology. The information theory, delineated by Claud Shannon, has no less importance when it was considered. Shannon put forwarded the apprehension of entropy to enumerate upper bounds in transmission rates in telephonic channels, in optical communication, and in wireless. The prestigious feature of entropy is that it entitles the amount of uncertainty in a system. The substantial participation of this paper is to explore characteristics of graph entropies and then keep moving forward to talk about the formation of coronoid polycyclic aromatic hydrocarbons. Likewise, we estimate entropies through precise topological indices established on degree of terminal nodes.

Highlights

Consider D (DV, DE) be a graph containing DV and DE as the vertex set and the edge set of D correspondingly. e size and the order of D are expressed by m and n correspondingly, and 􏽢I(a) is characterized as the degree of any vertex a
In QSPR/QSAR discussions, topological indices are applied to connect the biological functions of the anatomies with their corporeal properties like distortion, strain energy, stability, and melting point. ese determinations can be accomplished by employing degree-based indices as these indices have clarity of decision and rapidity
We proposed a new approach to estimate the entropy by estimating its topological indices. e degree-based entropy can be exerted to structural chemistry, ecological networks, biology, national security, social network, and so on

Summary

Introduction

Consider D (DV, DE) be a graph containing DV and DE as the vertex set and the edge set of D correspondingly. e size and the order of D are expressed by m and n correspondingly, and 􏽢I(a) is characterized as the degree of any vertex a. Consider D (DV, DE) be a graph containing DV and DE as the vertex set and the edge set of D correspondingly. E size and the order of D are expressed by m and n correspondingly, and 􏽢I(a) is characterized as the degree of any vertex a. Topological descriptors of a chemical structure are molecular descriptors. In QSPR/QSAR analyses, miscellaneous molecular descriptor is operated to correlate different biological and physico-chemical activities. We will talk about some degree-based indices. Is consideration was grown for analyzing the fundamental information of graphs. To determine the unpredictability of a scheme, entropy is used [1]. It was employed substantially in graphs and chemical networks

Results

Discussion

Conclusion