Connectivity, toughness, spanning trees of bounded degree, and the spectrum of regular graphs
Connectivity, toughness, spanning trees of bounded degree, and the spectrum of regular graphs
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DOI：
10.1007/s10587-016-0300-z
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发表时间：
2016-02
影响因子：
0.5
通讯作者：
S. Cioabă;Xiaofeng Gu
中科院分区：
文献类型：
--
作者：
S. Cioabă;Xiaofeng Gu
图的特征值与图的许多组合性质有关。在他的基础工作中，费德勒展示了图的拉普拉斯特征值和特征向量与其顶点连通性和边连通性之间的密切联系。我们给出了正则图的谱与其他组合参数之间的联系的一些新结果，如它的广义连通性、韧性和有界度生成树的存在性。
The eigenvalues of graphs are related to many of its combinatorial properties. In his fundamental work, Fiedler showed the close connections between the Laplacian eigenvalues and eigenvectors of a graph and its vertex-connectivity and edge-connectivity.We present some new results describing the connections between the spectrum of a regular graph and other combinatorial parameters such as its generalized connectivity, toughness, and the existence of spanning trees with bounded degree.