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两类冠图的Laplacian谱

DOI: 10.3969/j.issn.1006-7043.201308055

Keywords: 冠图, Laplacian矩阵, Laplacian特征多项式, L-谱, 生成树数目, Kirchhoff指数

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Abstract:

图的谱蕴含着图的许多信息。冠图是一种比较复杂的图, 冠图的谱更加难以计算。文中定义了两类冠图, 分别是:图G1和G2的剖分图的冠点图G1◇G2和剖分图的冠边图G1☆G2。应用分块矩阵、矩阵的coronal、克罗内克积证明了两类冠图的Laplacian谱可以表示为原图G1和G2的Laplacian谱;并给出了两类冠图的生成树数目以及Kirchhoff指数。

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