Sharp Bounds of First Zagreb Coindex for $F$-Sum Graphs

Abstract

Let G = V E , E G be a connected graph with vertex set V G and edge set E G . For a graph G, the graphs S(G), R(G), Q(G), and T(G) are obtained by applying the four subdivisions related operations S, R, Q, and T, respectively. Further, for two connected graphs G 1 and G 2 , G 1 + F G 2 are F -sum graphs which are constructed with the help of Cartesian product of F G 1 and G 2 , where F ∈ S , R , Q , T . In this paper, we compute the lower and upper bounds for the first Zagreb coindex of these F -sum (S-sum, R-sum, Q-sum, and T-sum) graphs in the form of the first Zagreb indices and coincides of their basic graphs. At the end, we use linear regression modeling to find the best correlation among the obtained results for the thirteen physicochemical properties of the molecular structures such as boiling point, density, heat capacity at constant pressure, entropy, heat capacity at constant time, enthalpy of vaporization, acentric factor, standard enthalpy of vaporization, enthalpy of formation, octanol-water partition coefficient, standard enthalpy of formation, total surface area, and molar volume.

Reverse Zagreb Indices and Their Application in the Evaluation of Physiochemical Properties of Anticancer/Antibacterial Drugs

“…Further studies were carried out in refs − . In this article, we perform regression analysis on some antibacterial or anticancer drugs.…”

Wiener Energies of Fuzzy Graphs with Application in Total Quality Management

“…In 1972, Gutman and Trinajstic [19] introduced the Zagreb index, a degree based index, for crisp graph which is used to calculate π-electron energy related to molecular graphs. For the applications of topological indices, refer [22,23,27,28,44]. Kale and Minirani [23] defined fuzzy first Zagreb index, second Zagreb index, hyper Zagreb index and corresponding fuzzy Zagreb matrices along with fuzzy Zagreb energies.…”