论文标题
图形拉普拉斯的极端特征值
On extremal eigenvalues of the graph Laplacian
论文作者
论文摘要
G. Berkolaiko，J.B。Kennedy，P。Kurasov和D. Mugnolo在2017年建立了Laplacian特征值的上和下部估计值。这两种估计都只能通过高度退化的特征值同时实现，我们称之为最大程度地退化。通过与2011年的I. Kac和V. pivovarchik证明的最大特征值多样性相比，我们表征了表现出最大变性特征值的图形家族，我们称之为套索树，即通过将套索图与某些人的某些人物相结合。
Upper and lower estimates of eigenvalues of the Laplacian on a metric graph have been established in 2017 by G. Berkolaiko, J.B. Kennedy, P. Kurasov and D. Mugnolo. Both these estimates can be achieved at the same time only by highly degenerate eigenvalues which we call maximally degenerate. By comparison with the maximal eigenvalue multiplicity proved by I. Kac and V. Pivovarchik in 2011 we characterize the family of graphs exhibiting maximally degenerate eigenvalues which we call lasso trees, namely graphs constructed from trees by attaching lasso graphs to some of the vertices.
