Abstract
A molecular descriptor is a mathematical measure that associates a molecular graph with some real numbers and predicts the various biological, chemical, and structural properties of the underlying molecular graph. Wiener (1947) and Trinjastic and Gutman (1972) used molecular descriptors to find the boiling point of paraffin and total π -electron energy of the molecules, respectively. For molecular graphs, the general sum-connectivity and general Randić are well-studied fundamental topological indices (TIs) which are considered as degree-based molecular descriptors. In this paper, we obtain the bounds of the aforesaid TIs for the generalized F -sum graphs. The foresaid TIs are also obtained for some particular classes of the generalized F -sum graphs as the consequences of the obtained results. At the end, 3 D -graphical presentations are also included to illustrate the results for better understanding.
Highlights
A molecular descriptor called by the topological index (TI) is a function from the set of graphs to the set of real numbers
We extend this study by computing the bounds of the general sum-connectivity and general Randicindices for the generalized F-sum graphs
We find out the sharp bounds of general sum-connectivity index (GSCI) and general Randicindex (GRI) of generalized F-sum graphs
Summary
A molecular descriptor called by the topological index (TI) is a function from the set of (molecular) graphs to the set of real numbers. TIs are studied as a subtopic of chemical graph theory to predict the chemical reactions, biological attributes, and physical features of the compounds in theoretical chemistry, toxicology, pharmaceutical industry, and environmental chemistry, see [1]. [13] defined the four subdivision-related operations (S11, S21, S31, and S41) on a molecular graph M and obtained the Wiener indices of the resultant graphs S11(M), S21(M), S31(M), and S41(M). Deng et al [15] and Akhter and Imran [16] computed the 1st and 2nd Zagreb and general sum-connectivity indices of the. We extend this study by computing the bounds (upper and lower) of the general sum-connectivity and general Randicindices for the generalized F-sum graphs. For a real number α and (molecular) graph M, the general sum-connectivity index (GSCI) and general Randicindex (GRI) are χα(M) dM x1 + dM x2α, x1 ,x2 εE(M).
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