Let ${\mathcal{G}}_{n,\beta }$ be the set of simple graphs of order n with given matching number β. In this paper, we characterize the extremal graphs with maximal $A_{\alpha }$-spectral radius in ${\mathcal{G}}_{n,\beta }$ for $0\le \alpha <1$, which generalizes the results for adjacency matrix in [Feng L, Yu G, Zhang X-D. Spectral radius of graphs with given matching number. Linear Algebra Appl. 2007;422:133–138, Theorem 1.1] and signless Laplacian matrix in [Yu G. On the maximal signless Laplacian spectral radius of graphs. Proc Japan Acad Ser A. 2018, Theorem 2.5].

中文翻译：

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具有给定匹配数的图的最大 Aα 谱半径

让${\mathcal{G}}_{n,\beta }$是具有给定匹配数β的n阶简单图集。在本文中，我们用极大值来表征极值图${\mathrm{一种}}_{\alpha }$-光谱半径${\mathcal{G}}_{n,\beta }$为了$0\le \alpha <\mathrm{1个}$, 它概括了 [Feng L, Yu G, Zhang XD. 中邻接矩阵的结果。具有给定匹配数的图的谱半径。线性代数应用。2007;422:133–138，定理 1.1] 和 [Yu G. 中的无符号拉普拉斯矩阵。关于图的最大无符号拉普拉斯谱半径。Proc Japan Acad Ser A. 2018，定理 2.5]。