Abstract
For any graph G, the Sombor index is defined as \(SO(G) = \sum \nolimits _{uv\in E(G)} \sqrt{d_G ^2 (u) + d_G ^2 (v)} \), where \(d_G (u)\) is the degree of the vertex u in G. In this paper, we determine the minimum Sombor index of trees of order \(n\ge 7\) with \(p\ge 3\) pendant vertices, which gives the partial solution for the open problem Das et al. (Mathematics 9:#1202, 2021). Our results also extend the results Liu et al. (Int J Quantum Chem 121: #e26689, 2021), about the minimum value of the Sombor index of chemical trees of order n with p pendant vertices.
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Communicated by Leonardo de Lima.
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Maitreyi, V., Elumalai, S., Balachandran, S. et al. The minimum Sombor index of trees with given number of pendant vertices. Comp. Appl. Math. 42, 331 (2023). https://doi.org/10.1007/s40314-023-02479-4
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DOI: https://doi.org/10.1007/s40314-023-02479-4