Brualdi and Hoffman [On the spectral radius of (0, 1)-matrices. Linear Algebra Appl. 1985;65:133–146] proposed the problem of determining the maximal spectral radius of graphs with a given size. In this paper, we consider the Brualdi–Hoffman-type problem for graphs with a given matching number. The maximal Q-spectral radius of graphs with a given size and matching number is obtained, and the corresponding extremal graphs are completely determined.

中文翻译：

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给定大小和匹配数的图的Q-谱半径的极值问题

Brualdi 和 Hoffman [关于 (0, 1)-矩阵的谱半径。线性代数应用。1985;65:133–146] 提出了确定给定尺寸图的最大谱半径的问题。在本文中，我们考虑具有给定匹配数的图的 Brualdi–Hoffman 型问题。得到给定大小和匹配数的图的最大Q谱半径，并完全确定对应的极值图。