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Extremal values of the atom-bond sum-connectivity index in bicyclic graphs

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Abstract

Let G be a graph with V(G) and E(G), as vertex set and edge set respectively. The atom-bond sum-connectivity index is a degree-based topological index which is defined as

$$\begin{aligned} ABS(G)=\sum \limits _{uv\in E(G)}\sqrt{\dfrac{d_u+d_v-2}{d_u+d_v}}, \end{aligned}$$

where the degree of the vertex u is denoted by \(d_u\). In this article, our focus lies on investigating the maximum value of atom-bond sum-connectivity among the class of bicyclic graphs on n vertices. In addition, the role of atom-bond sum-connectivity in explaining structure–property relationship is also demonstrated.

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Acknowledgements

The authors express their sincere gratitude to the anonymous reviewers for their great insightful comments and suggestions, which have significantly improved the presentation of our manuscript. Sourav Mondal is supported by the Postdoctoral Research Program of Sungkyunkwan University (2023).

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Author notes

  1. Kannan Aarthi, Suresh Elumalai, Selvaraj Balachandran and Sourav Mondal have contributed equally to this work.

Authors and Affiliations

  1. Department of Mathematics, College of Engineering and Technology, Faculty of Engineering and Technology, SRM Institute of Science and Technology, Kattankulathur, Chengalpattu, Tamil Nadu, 603203, India

    Kannan Aarthi, Suresh Elumalai & Sourav Mondal

  2. Department of Mathematics, School of Arts, Sciences and Humanities, SASTRA Deemed University, Thanjavur, Tamil Nadu, 613401, India

    Selvaraj Balachandran

  3. Department of Mathematics, Sungkyunkwan University, Suwon, 16419, Republic of Korea

    Sourav Mondal

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  1. Kannan Aarthi
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Correspondence to Suresh Elumalai.

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Aarthi, K., Elumalai, S., Balachandran, S. et al. Extremal values of the atom-bond sum-connectivity index in bicyclic graphs. J. Appl. Math. Comput. 69, 4269–4285 (2023). https://doi.org/10.1007/s12190-023-01924-1

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