Computing Correlation among the Graphs under Lexicographic Product via Zagreb Indices

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.

Topological Entropy Characterization, NMR and ESR Spectral Patterns of Coronene-Based Transition Metal Organic Frameworks

“…A product of chemical graph theory is the topological index which is a structural descriptor that aids in characterizing the underlying connectivities of complex molecular structures, − thereby providing tools for the prediction of the properties. − Furthermore, the International Union of Pure and Applied Chemistry (IUPAC) has also recommended the topological indices for interpreting the descriptions of these MOF crystal structures, as the topology of every MOF structure is unique pertaining to its arrangement of atoms and bonds . A large number of topological indices that are based on topological distances and vertex degrees have been developed over the years in order to predict the physicochemical properties and activities of molecules. − Likewise, graph entropy based on Shannon’s definition is an information–theoretic index that associates deterministic and probabilistic distributions to the topological index functions in order to characterize the underlying structural orders and complexities of molecular structures. − The entropy-based indices of various molecular frameworks have gained interest in recent years. − In this study, we obtain the degree and degree-sum-based topological indices and their entropies for three different structures of coronene-based metal organic frameworks which play a significant role in understanding the tunable properties of MOFs and in addressing the complexity of their structural geometries. Furthermore, we employ distance degree vector sequences together with their symmetry features to obtain the typical NMR and ESR spectroscopic signatures which enable contrast of these structures through potential spectroscopic studies in the future.…”

Investigation of Atom-Bond Connectivity Indices of Line Graphs Using Subdivision Approach

“…ese indices are also signi cant in quantitative structure-property relationship (QSPR) and quantitative structure-activity relationship (QSAR) (see [4,5]).…”

Retracted: Computing Correlation among the Graphs under Lexicographic Product via Zagreb Indices

“…Tis article has been retracted by Hindawi following an investigation undertaken by the publisher [1]. Tis investigation has uncovered evidence of one or more of the following indicators of systematic manipulation of the publication process:…”