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Nonregular graphs of odd maximum degree with maximum spectral radius
Let $ρ(n,d)$ denote the maximum adjacency spectral radius among all connected nonregular graphs of order $n$ and maximum degree $d$. A graph attaining this maximum is called an extremal graph. Liu [J. Combin. Theory Ser. B, 2024] determined the extremal graphs for $d=3,4$ and formulated two conjec
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