Several Topological Indices of Random Caterpillars

Panpan Zhang () and Xiaojing Wang ()
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Panpan Zhang: University of Pennsylvania
Xiaojing Wang: University of Connecticut

Methodology and Computing in Applied Probability, 2022, vol. 24, issue 3, 1773-1789

Abstract: Abstract In chemical graph theory, caterpillar trees have been an appealing model to represent the molecular structures of benzenoid hydrocarbon. Meanwhile, topological index has been thought of as a powerful tool for modeling quantitative structure-property relationship and quantitative structure-activity between molecules in chemical compounds. In this article, we consider a class of caterpillar trees that are incorporated with randomness, called random caterpillars, and investigate several popular topological indices of this random class, including Zagreb index, Randić index and Wiener index, etc. Especially, a central limit theorem is developed for the asymptotic distribution of the Zagreb index of random caterpillars.

Keywords: Caterpillar tree; Chemical graph theory; Central limit theorem; Martingale; Random caterpillars; Topological index; Primary: 05C80; 92E10; Secondary: 50C10; 60F05 (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s11009-021-09895-1

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