This paper is devoted to the problem of isomorphism in graphs and proposes a method based on time response of a differential equation. First it is shown that the solution of a differential equation obtaining from a Laplacian matrix can be used as an index and the proof is presented. Then a search algorithm is proposed to find out that the two graphs are isomorphic and there is a permutation matrix describing relations between the graphs. The search algorithm depends on eigenvalues of the Laplacian matrix. For a Laplacian matrix with repeated eigenvalues, Greshgorin theorem is used to convert it to a matrix with non-repeated eigenvalues. This is performed by adding loops to vertices, so that they have separated Greshgorin bands. Then the time response of the differential equation is checked. The proposed method is performed on co-spectral graphs and results are described.

中文翻译：

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图同构问题的基于时间的解决方案

本文致力于解决图中的同构问题，并提出了一种基于微分方程时间响应的方法。首先证明了从拉普拉斯矩阵得到的微分方程的解可以用作指标并给出证明。然后提出一种搜索算法，找出两个图是同构的，并且存在一个描述图之间关系的置换矩阵。搜索算法取决于拉普拉斯矩阵的特征值。对于具有重复特征值的拉普拉斯矩阵，使用 Greshgorin 定理将其转换为具有非重复特征值的矩阵。这是通过向顶点添加循环来执行的，以便它们分离 Greshgorin 带。然后检查微分方程的时间响应。