Abstract
Numerous studies based on mathematical models and tools indicate that there is a strong inherent relationship between the chemical properties of the chemical compounds and drugs with their molecular structures. In the last two decades, the graph-theoretic techniques are frequently used to analyse the various physicochemical and structural properties of the molecular graphs which play a vital role in chemical engineering and pharmaceutical industry. In this paper, we compute Zagreb indices of the generalized sum graphs in the form of the different indices of their factor graphs, where generalized sum graphs are obtained under the operations of subdivision and strong product of graphs. Moreover, the obtained results are illustrated with the help of particular classes of graphs and analysed to find the efficient subclass with dominant indices.
Highlights
In many fields various physicochemical and structural properties such as melting point, boiling point, chemical bonds, bond energy, solubility, surface tension, critical temperature, connectivity, stability, density, and polarizability are studied with the help of various topological index (TI)
Gutman and Trinajstic [5] calculated total π-electrons energy of the molecules through a degree-based TI called as the first Zagreb index (FZI). ey studied the various properties of the second Zagreb index (SZI) in the same paper
We study the generalized Φ-sum graphs which are obtained under the operation of strong product on the graphs Φk(G1) and G2, where Φk ∈ Sk, Rk, Qk, Tk and k is some counting number
Summary
In many fields (chemistry, physics, computer science, and electrical networks) various physicochemical and structural properties such as melting point, boiling point, chemical bonds, bond energy, solubility, surface tension, critical temperature, connectivity, stability, density, and polarizability are studied with the help of various TIs (degree-based, distance-based, and polynomial-based). Liu et al [11] constructed Φ-sum graphs with the help of the Cartesian product on the graphs Φ(G1) and G2 and calculated the first general Zagreb index for these graphs, i.e., Mα1G1+Φ1 G2. Liu et al [12] introduced the generalized Φ-sum (Φk-sum) graphs with the help of the Cartesian product on the graphs Φk(G1) and G2, where k represents some integral value They calculated the mathematical expressions of the Zagreb indices for these graphs, i.e., M1 G1+Φ1 G2 and M2 G1+Φk G2 . Awais et al [13, 14] computed the forgotten topological and hyper-Zagreb indices of generalized F-sum graphs based on Cartesian product in terms of its factor graphs. A comparison is organized of the generalized Φ-sum graphs G1⊠Sk G2 , G1⊠Rk G2 , G1⊠Qk G2 , and G1⊠Tk G2 with respect to both the Zagreb indices (M1 and M2). e rest of the paper is settled as follows: Section 2 covers basic notions, Section 3 predicated on main results, and conclusively Section 4 included the application and conclusion.”
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