Abstract
Abstract The quantitative structures activity relationships (QSAR) and quantitative structures property relationships (QSPR) between the chemical compounds are studied with the help of topological indices (TI’s) which are the fixed real numbers directly linked with the molecular graphs. Gutman and Trinajstic (1972) defined the first degree based TI to measure the total π-electrone energy of a molecular graph. Recently, Ali and Trinajstic (2018) restudied the connection based TI’s such as first Zagreb connection index, second Zagreb connection index and modified first Zagreb connection index to find entropy and accentric factor of the octane isomers. In this paper, we study the modified second Zagreb connection index and modified third Zagreb connection index on the T-sum (molecular) graphs obtained by the operations of subdivision and product on two graphs. At the end, as the applications of the obtained results for the modified Zagreb connection indices of the T-sum graphs of the particular classes of alkanes are also included. Mainly, a comparision among the Zagreb indices, Zagreb connection indices and modified Zagreb connection indices of the T-sum graphs of the particular classes of alkanes is performed with the help of numerical tables, 3D plots and line graphs using the statistical tools.
Highlights
A topological index (TI) is represented as a graphical invariant in chemical graph theory with graphical termsIn addition, the quantitative structures activity relationships (QSAR) and quantitative structures property relationships (QSPR) are useful in the study of molecules with the help of these topological indices (TI’s)
The quantitative structures activity relationships (QSAR) and quantitative structures property relationships (QSPR) between the chemical compounds are studied with the help of topological indices (TI’s) which are the fixed real numbers directly linked with the molecular graphs
We study the modified second Zagreb connection index and modified third Zagreb connection index on the T-sum graphs obtained by the operations of subdivision and product on two graphs
Summary
A topological index (TI) is represented as a graphical invariant in chemical graph theory with graphical terms. Classical Zagreb indices was defined in Gutman and Trinajstic (1972) and Gutman et al (1975) These are very well known and frequently used in the study of chemical graph theory. These are called first Zagreb index (M (G)) and second. Many TI’s have been explored with their properties and they have revolutionized the fruitful results in the study of science especially in the lattest field of cheminformatics that is the combination of three subjects Mathematics, Chemistry and Information Technology (Borovicanin et al, 2017; Das and Gutman, 2004; Liu et al, 2019a, 2019e, 2019f; Shirinivas et al, 2010; Todeschini and Consonni, 2002), degree based. Tang et al (2019) k derived the exact formulas of the Zagreb connection indices ( ) ZC1(G), ZC2 (G)& ZC1* (G) of the T-sum graphs with the help of these subdivision-related operations. The current article is framed as follows: Section II presents the preliminary definitions of the classical/novel Zagreb indices, Section III holds the general results and section IV covers the applications and conclusion
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