The number of spanning trees of a graph G is the total number of distinct spanning subgraphs of G that are trees. Feng et al. determined the maximum number of spanning trees in the class of connected graphs with n vertices and matching number \(\beta \) for \(2\le \beta \le n/3\) and \(\beta =\lfloor n/2\rfloor \). They also pointed out that it is still an open problem to the case of \(n/3<\beta \le \lfloor n/2\rfloor -1\). In this paper, we solve this problem completely.

中文翻译：

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具有给定匹配数的图的最大生成树数

图G的生成树数是G的树的不同生成子图的总数。冯等。确定生成树的最大数量在类与连通图的Ñ顶点和匹配数\（\测试\）为\（2 \文件\测试\文件N / 3 \）和\（\的β= \ lfloor N / 2 \ rfloor \）。他们还指出，对于\（n / 3 <\ beta \ le \ lfloor n / 2 \ rfloor -1 \）来说，这仍然是一个未解决的问题。在本文中，我们完全解决了这个问题。