Abstract
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.
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