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Open Access Research Article

Investigating several statistical parameters of topological indices for random caterpillars and related graphs

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pp. 2223–2240Vol. 29Issue 6June 2026DOI: 10.47974/JDMSC-2402 Crossmark XML
Received:
01 Jan 2026
Published Online:
20 Jun 2026
Article type:
Research Article
Language:
EN
Article no.:
JDMSC-2402
Pages:
2223–2240

Abstract

In the dynamic fields of mathematical chemistry and chemoinformatics, caterpillar trees are widely employed as a foundational tool for modeling the structures of unbranched benzenoid hydrocarbon molecules. They are a renowned topological index used to model QSPR and QSAR between molecules. This article explores into an intriguing class of caterpillar trees that integrates randomness, offering a fresh perspective on the Zagreb index and its generalizations. We meticulously compute the skewness and kurtosis associated with the Zagreb index, presenting analytical expressions for the expected value of its generalized form. Moreover, the asymptotic behavior of the generalized Zagreb index is characterized and analyzed for caterpillars generated randomly through the application of the Martingale Central Limit Theorem. Finally, we conduct thorough numerical experiments that analyze the behaviors of statistical parameters in this unique class.

Keywords

Subject Classifications

05C0505C0905C1205C8005C92

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