Smith Normal Form and Acyclic Matrics
组合数学
2007-05-23 v1
摘要
An approach, based on the Smith Normal Form, is introduced to study the spectra of symmetric matrices with a given graph. The approach serves well to explain how the path cover number (resp. diameter of a tree T) is related to the maximum multiplicity occurring for an eigenvalue of a symmetric matrix whose graph is T (resp. the minimum number q(T) of distinct eigenvalues over the symmetric matrices whose graphs are T). The approach is also applied to a more general class of connected graphs G, not necessarily trees, in order to establish a lower bound on q(G).
引用
@article{arxiv.math/0508265,
title = {Smith Normal Form and Acyclic Matrics},
author = {Bryan L. Shader and In-Jae Kim},
journal= {arXiv preprint arXiv:math/0508265},
year = {2007}
}
备注
24 pages