Abstract
The arithmetic-geometric spectral radius of a graph G is the largest eigenvalue of the arithmetic-geometric matrix of G whose (u, v)-entry is \(\frac{d_u+d_v}{2\sqrt{d_ud_v}}\) if u and v are adjacent and 0 otherwise for \(u,v\in V(G)\), where \(d_u\) denotes the degree of vertex u in G. We determine the graphs with the largest and the next largest arithmetic-geometric spectral radii over all n-vertex bicyclic graphs with \(n\ge 5\).
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Acknowledgements
This work was supported by Guangdong Basic and Applied Basic Research Foundation (No. 2021A1515010028).
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Communicated by Leonardo de Lima.
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Yuan, Y. On the arithmetic-geometric spectral radius of bicyclic graphs. Comp. Appl. Math. 42, 304 (2023). https://doi.org/10.1007/s40314-023-02449-w
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DOI: https://doi.org/10.1007/s40314-023-02449-w