Abstract
A topological index is a numerical quantity associated with the molecular structure of a chemical compound. This number remains fixed with respect to the symmetry of a molecular graph. Diverse research studies have shown that the topological indices of symmetrical graphs are interrelated with several physiochemical properties such as boiling point, density, and heat of formation. Peripherality is also an important tool to study topological aspects of molecular graphs. Recently, a bond-additive topological index called the Mostar index that measures the peripherality of a graph is investigated which attained wide attention of researchers. In this article, we compute the Mostar index of cycle-related structures such as the Jahangir graph and the cycle graph with chord.
Highlights
Graph theory is being extensively used in mathematical chemistry for the numerical formulation of chemical compounds by representing atoms as vertices and bonds as edges. e topological index (TI) of a molecular graph is a numerical quantity associated with the molecular structure of a chemical compound [1, 2]. ese quantities are well correlated with physicochemical properties and are used as a tool to predict quantitative structure-activity relationships and quantitative structure-property relationships (QSAR/ QSPR) [3, 4]
QSAR and QSPR techniques have been widely used to study the structural properties of a molecule and its biological activity [5, 6]. e TIs are majorly classified into two types, namely, degree-based and distance-based or bond-additive topological indices. e degree-based TIs focus on the role of incident bonds towards the molecular structure [7, 8] whereas the distance-based TIs emphasize on the contribution of distances between atoms towards the structure of a compound [9]. e introduction of the first distance-based TI by Wiener in [10] pointed its significance towards the physicochemical properties of the compound
E physicochemical properties such as boiling point and melting point were shown in correlation with the Wiener index [11]
Summary
Graph theory is being extensively used in mathematical chemistry for the numerical formulation of chemical compounds by representing atoms as vertices and bonds as edges. e topological index (TI) of a molecular graph is a numerical quantity associated with the molecular structure of a chemical compound [1, 2]. ese quantities are well correlated with physicochemical properties and are used as a tool to predict quantitative structure-activity relationships and quantitative structure-property relationships (QSAR/ QSPR) [3, 4]. Graph theory is being extensively used in mathematical chemistry for the numerical formulation of chemical compounds by representing atoms as vertices and bonds as edges. E topological index (TI) of a molecular graph is a numerical quantity associated with the molecular structure of a chemical compound [1, 2]. E TIs are majorly classified into two types, namely, degree-based and distance-based or bond-additive topological indices. To measure the peripherality of graphs, Doslic et al proposed a new bond-additive topological index called the Mostar index [18]. E Mostar index measures peripheral atoms and bonds to determine the physical and chemical properties of a molecular graph. ⎧⎨ m2n2 + 2m2n − mn2 + m2 − 6mn − 5m, if n odd, Mo Jn,m ⎩ m2n2 + 2m2n − mn2 + m2 − 5mn − m, if n even. (4)
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