BOUNDS FOR THE EXTREME EIGENVALUES OF THE LAPLACIAN AND SIGNLESS LAPLACIAN OF A GRAPH

L. Yu. Kolotilina

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BOUNDS FOR THE EXTREME EIGENVALUES OF THE LAPLACIAN AND SIGNLESS LAPLACIAN OF A GRAPH

机译：图的拉普拉斯和无符号拉普拉斯极值特征的界

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摘要

The paper suggests a new approach to deriving lower bounds for the Laplacian spectral radius and upper bounds for the smallest eigenvalue of the signless Laplacian of an undirected simple r-partite graph on n vertices, 2 ≤ r ≤ n. The approach is based on inequalities for the extreme eigenvalues of a block-partitioned Hermitian matrix, established earlier, and on the Rayleigh principle. Specific lower and upper bounds generalizing known results and extending them from r = 2 to r ≥ 1 are considered, and the cases where these bounds are sharp are described.

机译：本文提出了一种新的方法来推导n个顶点（2≤r≤n）上无向简单r局部图的无符号拉普拉斯算子的拉普拉斯谱半径的下界和最小特征值的上限。该方法基于较早建立的块划分的Hermitian矩阵的极值特征值的不等式，并且基于Rayleigh原理。考虑了将已知结果推广并将其从r = 2扩展到r≥1的特定下限和上限，并描述了这些界限较明显的情况。

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《Journal of Mathematical Sciences》 |2012年第6期|p.803-813|共11页
作者
L. Yu. Kolotilina;
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作者单位

Department of the Steklov Mathematical Institute, St.Petersburg, Russia;

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BOUNDS FOR THE EXTREME EIGENVALUES OF THE LAPLACIAN AND SIGNLESS LAPLACIAN OF A GRAPH

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