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On degree-based topological indices of symmetric chemical structures. (English) Zbl 1423.92253
Summary: A Topological index also known as connectivity index is a type of a molecular descriptor that is calculated based on the molecular graph of a chemical compound. Topological indices are numerical parameters of a graph which characterize its topology and are usually graph invariant. In QSAR/QSPR study, physico-chemical properties and topological indices such as Randić, atom-bond connectivity (ABC) and geometric-arithmetic (GA) index are used to predict the bioactivity of chemical compounds. Graph theory has found a considerable use in this area of research. In this paper, we study HDCN1\((m,n)\) and HDCN2\((m,n)\) of dimension \(m\), \(n\) and derive analytical closed results of general Randić index \(R_\alpha(\mathcal G)\) for different values of \(\alpha\). We also compute the general first Zagreb, ABC, GA, \(ABC_4\) and \(GA_5\) indices for these Hex derived cage networks for the first time and give closed formulas of these degree-based indices.
MSC:
92E10 Molecular structure (graph-theoretic methods, methods of differential topology, etc.)
05C90 Applications of graph theory
05C40 Connectivity
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