论文标题
图形laplacians的特征值通过排名一扰动
Eigenvalues of graph Laplacians via rank-one perturbations
论文作者
论文摘要
我们展示了图形laplacian的频谱如何相对于某种类型的等级一扰动。我们应用我们的发现来为Kirchhoff的基质树定理的光谱版本提供新的简短证明，并为Laplacians的特征多项式提供了许多众所周知的图形系列，包括完整的，完整的多部分和阈值图。
We show how the spectrum of a graph Laplacian changes with respect to a certain type of rank-one perturbation. We apply our finding to give new short proofs of the spectral version of Kirchhoff's Matrix Tree Theorem and known derivations for the characteristic polynomials of the Laplacians for several well known families of graphs, including complete, complete multipartite, and threshold graphs.
