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Smallest ABS index of unicyclic graphs with given girth

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Abstract

The atom-bond sum-connectivity index of a graph G is defined as

$$\begin{aligned} ABS(G) = {\sum \limits _{xy\in E(G)}} \sqrt{\frac{{d_x}+{d_y}-2}{{d_x}+{d_y}}}, \end{aligned}$$

where \({d_x}\) is the degree of the vertex x in G. In this paper, we study the ABS index of unicyclic graphs with a specified girth and determine the smallest, second smallest, third smallest, and fourth smallest ABS index. We also identify the graphs that achieve these extremal values. In addition, the ABS index is found to have significant potential in structure–property modelling for some compounds containing cyclic substructures.

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Acknowledgements

The authors would like to thank the anonymous referees for their insightful comments and suggestions, which have significantly improved the presentation of this research. The fourth author is supported by the Postdoctoral Research Program of Sungkyunkwan University (2023).

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Authors and Affiliations

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

    Palaniyappan Nithya, Suresh Elumalai & Sourav Mondal

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

    Selvaraj Balachandran

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

    Sourav Mondal

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  1. Palaniyappan Nithya
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Correspondence to Suresh Elumalai.

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Nithya, P., Elumalai, S., Balachandran, S. et al. Smallest ABS index of unicyclic graphs with given girth. J. Appl. Math. Comput. 69, 3675–3692 (2023). https://doi.org/10.1007/s12190-023-01898-0

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  • DOI: https://doi.org/10.1007/s12190-023-01898-0

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