Abstract
It is considered that there is a fascinating issue in theoretical chemistry to predict the physicochemical and structural properties of the chemical compounds in the molecular graphs. These properties of chemical compounds (boiling points, melting points, molar refraction, acentric factor, octanol-water partition coefficient, and motor octane number) are modeled by topological indices which are more applicable and well-used graph-theoretic tools for the studies of quantitative structure-property relationships (QSPRs) and quantitative structure-activity relationships (QSARs) in the subject of cheminformatics. The π -electron energy of a molecular graph was calculated by adding squares of degrees (valencies) of its vertices (nodes). This computational result, afterwards, was named the first Zagreb index, and in the field of molecular graph theory, it turned out to be a well-swotted topological index. In 2011, Vukicevic introduced the variable sum exdeg index which is famous for predicting the octanol-water partition coefficient of certain chemical compounds such as octane isomers, polyaromatic hydrocarbons (PAH), polychlorobiphenyls (PCB), and phenethylamines (Phenet). In this paper, we characterized the conjugated trees and conjugated unicyclic graphs for variable sum exdeg index in different intervals of real numbers. We also investigated the maximum value of SEIa for bicyclic graphs depending on a > 1 .
Highlights
In chemical graph theory, molecules and macromolecules are represented by graphs wherein vertices correspond to the atoms, whereas edges represent the bonds between atoms [1, 2]
Physicochemical properties of chemical compounds such as relative enthalpy of formation, biological activity, boiling points, melting points, molar refraction, acentric factor, octanol-water partition coefficient, and motor octane number are modeled by topological indices in quantitative structure-property relation (QSPR) and quantitative structure-activity relation (QSAR) studies [4, 6,7,8]
Platt index was proposed in 1952 for predicting paraffin properties [10]. e π-electron energy of a molecular graph was calculated by adding square of degrees of its vertices in the year 1972. e same computational result, afterwards, was named the first Zagreb index, and in the field of molecular graph theory, it turned out to be a well-swotted topological index [11]
Summary
Molecules and macromolecules (such as organic compounds, nucleic acids, and proteins) are represented by graphs wherein vertices correspond to the atoms, whereas edges represent the bonds between atoms [1, 2]. Is topological index in the form of polynomial was proposed by Yarahmadi and Ashrafi, and they find its application in nanoscience [23] Chemical application of this index can be seen in the papers [12, 13, 15]. We investigated lower and upper bounds of unicyclic conjugated graphs with respect to the length of this cycle in different intervals. At the end of this paper, we find upper bounds of SEIa for bicyclic graphs.
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