Abstract
The exponential second Zagreb index of a graph G is defined as \(e^{M_2}(G)=\sum _{xy\in E(G)}e^{d_xd_y}\), where \(d_x\) is the degree of vertex x. Recently, Eliasi (Discrete Appl Math 307:172–179, 2022) posed a conjecture about (n, m)-graphs with maximum exponential second Zagreb index, when \(n\le m\le 2n-3\). In this paper, we prove that this conjecture holds for all graphs whose diameter is not equal to three.
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Acknowledgements
This work is supported by Mongolian Foundation for Science and Technology (Grant no. SHUTBIKHKHZG-2022/162).
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C.X., B.H. and L.B wrote the main manuscript text and C.X. prepared figures. All authors reviewed the manuscript.
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Xu, C., Horoldagva, B. & Buyantogtokh, L. The Exponential Second Zagreb Index of (n, m)-Graphs. Mediterr. J. Math. 20, 181 (2023). https://doi.org/10.1007/s00009-023-02387-1
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DOI: https://doi.org/10.1007/s00009-023-02387-1