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Journals / Hacettepe Journal of Mathematics and Statistics / 2026 / Volume: 55 Issue: 1

Effect of atom bond connectivity index on family of graphs under transformation

Rauf Irshad(COMSATS University Islamabad)0009-0004-9186-0774
Muhammad Hussain(COMSATS University Islamabad)0000-0003-1768-3111
Maqsood Ahmad(COMSATS University Islamabad)0000-0002-6858-3244
Pages
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Publication Date
2026-02-23
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Finally, we worked out several examples to check the accuracy of our results.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:The atom-bond connectivity ($ABC$) index is a well-studied degree-related topological index that investigates the physicochemical properties of chemical compounds.
📊
Key Findings & Data:It is a suitable predictor of stability and the strain energy of alkanes and cycloalkanes, respectively.
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Conclusion & Impact:Finally, we worked out several examples to check the accuracy of our results.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:atom bond connectivity index · extremal graph · networks

Abstract

The atom-bond connectivity ($ABC$) index is a well-studied degree-related topological index that investigates the physicochemical properties of chemical compounds. It is a suitable predictor of stability and the strain energy of alkanes and cycloalkanes, respectively. In this work, first, we identify vertices for different families of $n$-vertex network with complete graphs of any order to obtain a new transformation network. Analogously, we get a variety of transformed graphs. Later, we compute the $ABC$ index for the transformed graphs acquired by the above-described process. The results thus obtained help us provide the extremal results regarding the $ABC$ index for the transformation graphs under discussion. Finally, we worked out several examples to check the accuracy of our results.

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Cite This Article

Irshad, R., Hussain, M., Ahmad, M. (2026). Effect of atom bond connectivity index on family of graphs under transformation. Hacettepe Journal of Mathematics and Statistics, Volume: 55 Issue: 1. https://doi.org/10.15672/hujms.1509270

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