In [A note about cospectral graphs for the adjacency and normalized Laplacian matrices. Linear Multilinear Algebra. 2010;58(3-4):387–390], Butler constructed a family of bipartite graphs, which are cospectral for both the adjacency and the normalized Laplacian matrices. In this article, we extend this construction for generating larger classes of bipartite graphs, which are cospectral for both the adjacency and the normalized Laplacian matrices. Also, we provide a couple of constructions of non-bipartite graphs, which are cospectral for the adjacency matrices but not necessarily for the normalized Laplacian matrices.

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关于邻接和归一化拉普拉斯矩阵的余谱图的构建

在 [关于邻接和归一化拉普拉斯矩阵的余谱图的注释。线性多线性代数。2010;58(3-4):387–390]，Butler 构建了一个二部图族，它们对于邻接矩阵和归一化拉普拉斯矩阵都是协谱的。在本文中，我们扩展了这种构造以生成更大类别的二部图，这些二部图对于邻接矩阵和归一化拉普拉斯矩阵都是共谱的。此外，我们提供了一些非二分图的构造，它们对于邻接矩阵是协谱的，但对于归一化拉普拉斯矩阵不一定是协谱的。