Abstract
A topological index (TI) is a numerical descriptor of a molecule structure or graph that predicts its different physical, biological, and chemical properties in a theoretical way avoiding the difficult and costly procedures of chemical labs. In this paper, for two connected (molecular) graphs G 1 and G 2 , we define the generalized total-sum graph consisting of various (molecular) polygonal chains by the lexicographic product of the graphs T k G 1 and G 2 , where T k G 1 is obtained by applying the generalized total operation T k on G 1 with k ≥ 1 as some integral value. Moreover, we compute the different degree-based TIs such as first Zagreb, second Zagreb, forgotten Zagreb, and hyper-Zagreb. In the end, a comparison among all the aforesaid TIs is also conducted with the help of certain statistical tools for some particular families of generalized total-sum graphs under lexicographic product.
Highlights
Chemical graph theory is a fascinating branch of mathematical chemistry in which the structural formulas of the different chemicals or chemical compounds are modelled as chemical structures or graphs such as the vertices correspond to the atoms and edges represent the chemical bonds between them
Topological indices (TIs) are graph-theoretic tools which are widely used in chemical graph theory to study the various structural and chemical characteristics of the chemical graphs
In the subject of cheminformatics, these indices play a key role in the studies of the quantitative structure-property and quantitative structure-activity relationships which mathematically correlate the chemical properties with the physical structures of their chemical compounds
Summary
Chemical graph theory is a fascinating branch of mathematical chemistry in which the structural formulas of the different chemicals or chemical compounds are modelled as chemical structures or graphs such as the vertices correspond to the atoms and edges represent the chemical bonds between them. Topological indices (TIs) are graph-theoretic tools which are widely used in chemical graph theory to study the various structural and chemical characteristics (critical temperature, heat formation, density, extremal connectivity, unique classifications, and symmetric behaviours) of the chemical graphs. Gutman and Trinajsti (1972) [2] defined the 1st and 2nd Zagreb indices that are used to compute the different structure base characteristics of the molecular graphs. Ese Zagreb indices are used to measure the extent of branching of the carbon-atom skeleton of the various underlying chemical structures. For various results of the TIs on different chemical graphs, we refer to [6,7,8]
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