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本文利用图论方法并结合非负矩阵的有关经典结果,成功地给出了任意阶的非负方阵有以原点为中心的圆盘数值域的充要条件。 相似文献
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设T为含n个顶点的树,L(T)为其Laplace矩阵,L(T)的次小特征值α(T)称为T的代数连通度,Fiedlcr给出如下关于α(T)的界的经典结论α(Pn)≤α(T)≤α(Sn),其中Pn,Sn分别为含有n个顶点的路和星.Merris和Mass独立地证明了:α(T)=α(Sn)当且仅当T=Sn.通过重新组合由Fiedler向量所赋予的顶点的值,本给出上述不等式的新证明,并证明了:α(T)=α(Pn)当且仅当T=Pn。 相似文献
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In this Paper,the inertia of a symmetric Z-matrix is studied,and bounds of the number of its positive eigenvalues are obtained.Also the interlacing theorem for Schur complement of a symmetric Z-matrix is established,which can be considered as a generalization Cauchy interlacing theorem in some extent. 相似文献
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图的最小特征值定义为图的邻接矩阵的最小特征值,是刻画图结构性质的一个重要代数参数. 在所有给定阶数的补图为2-点或2-边连通的图中, 刻画了最小特征值达到极小的唯一图, 并给出了这类图最小特征值的下界. 相似文献
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The Laplacian spread of a graph is defined to be the difference between the largest eigenvalue and the second smallest eigenvalue of the Laplacian matrix of the graph. In our recent work, we have determined the graphs with maximal Laplacian spreads among all trees of fixed order and among all unicyclic graphs of fixed order, respectively. In this paper, we continue the work on Laplacian spread of graphs, and prove that there exist exactly two bicyclic graphs with maximal Laplacian spread among all bicyclic graphs of fixed order, which are obtained from a star by adding two incident edges and by adding two nonincident edges between the pendant vertices of the star, respectively. 相似文献