Irregularity Measures of Subdivision Vertex-Edge Join of Graphs

Jialin Zheng,Muhammad Ishaq,Muhammad Aamir,Adnan Aslam,Zahid Iqbal,Shehnaz Akhter,Muhammad Kashif Shafiq,Muhammad J Habib

doi:10.1155/2021/6673221

Abstract

The study of graphs and networks accomplished by topological measures plays an applicable task to obtain their hidden topologies. This procedure has been greatly used in cheminformatics, bioinformatics, and biomedicine, where estimations based on graph invariants have been made available for effectively communicating with the different challenging tasks. Irregularity measures are mostly used for the characterization of the nonregular graphs. In several applications and problems in various areas of research like material engineering and chemistry, it is helpful to be well-informed about the irregularity of the underline structure. Furthermore, the irregularity indices of graphs are not only suitable for quantitative structure-activity relationship (QSAR) and quantitative structure-property relationship (QSPR) studies but also for a number of chemical and physical properties, including toxicity, enthalpy of vaporization, resistance, boiling and melting points, and entropy. In this article, we compute the irregularity measures including the variance of vertex degrees, the total irregularity index, the σ irregularity index, and the Gini index of a new graph operation.

Highlights

Mathematical chemistry is showing assistance by providing the time-saving and competent tools for the characterizations of chemical compounds instead of any other data as input
Mathematical chemistry, and environmental sciences, these descriptors are used for the quantitative structure-activity relationship (QSAR)/quantitative structure-property relationship (QSPR) studies, where biological or chemical activities and physical properties of an underline structure are associated with its molecular structure. erefore, these descriptors are mostly quoted as molecular descriptors [4]
Among degree-based indices, irregularity measures may play an important role in chemistry, especially in the QSPR/QSAR studies [1, 10] as well as network theory [5, 11]. ese measures have been chosen to analyse the topological aspects of the underline structures; for instance, see [5, 10,11,12,13,14,15,16,17]

Summary

Introduction

Mathematical chemistry is showing assistance by providing the time-saving and competent tools for the characterizations of chemical compounds instead of any other data as input. Among degree-based indices, irregularity measures may play an important role in chemistry, especially in the QSPR/QSAR studies [1, 10] as well as network theory [5, 11]. Gutman provided some basic results for some irregularity measures of graphs in [15]. A topological index is said to be an irregularity measure if this has a nonzero value for a nonregular graph, and it has a value equal to zero for a regular graph.

Results

Conclusion