Eigenvalues of graph Laplacians via rank-one perturbations

Autor:	Klee, Steven, Stamps, Matthew T.
Rok vydání:	2020
Předmět:	Mathematics - Combinatorics
Druh dokumentu:	Working Paper
Popis:	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.
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2008.01669 Zobrazit plný text záznamu View this record from Arxiv