Let be a graph with Laplacian matrix . Denote by the permanent of . In this study, we investigate the problem of computing the permanent of the Laplacian matrix of nonbipartite graphs. We show that the permanent of the Laplacian matrix of some classes of nonbipartite graphs can be formulated as the composite of the determinants of two matrices related to those Laplacian matrices. In addition, some recursion formulas on are deduced.

中文翻译：

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计算非二部图的拉普拉斯矩阵的恒久

让是一个带有拉普拉斯矩阵的图。用的永久表示。在这项研究中，我们研究了计算非二部图的拉普拉斯矩阵的永久问题。我们表明，某些类别的非二部图的拉普拉斯矩阵的恒常性可以表示为与这些拉普拉斯矩阵相关的两个矩阵的行列式的复合。此外，还推导出了一些递归公式。