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.
Highlights
Ere are various types of topological index (TI) based on degree, distance, and polynomial, but degree-based topological indices (TIs) are more studied than others
The obtained results are illustrated with the help of the examples of the exact and bonded values for some particular F-sum graphs. e reset of the paper is organized as follows: Section 2 includes the basic definitions and notions, Section 3 contains the main results of our work, and Section 4 presents particular examples related to the main results
We discussed the main results of the first Zagreb coindex on the F-sum graphs which will be denoted by M−
Summary
Ere are various types of TIs based on degree, distance, and polynomial, but degree-based TIs are more studied than others (see the latest survey [6]). Suppose that G1 and G2 are two connected graphs; their F-sum graphs are denoted by G1+FG2 and defined with vertex set |V(G1+SG2)| V(G1) ∪ E(G1) × V(G2) and edge set as the vertices (u1, u2) and (v1, v2) of G1+FG2 are joined iff (i) u1 v1 ∈ V(G1) and u2∽v2 ∈ G2.
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