Smith Normal Form and Acyclic Matrics
| dc.creator | Shader, Bryan L. | |
| dc.creator | Kim, In-Jae | |
| dc.date | 2005-08-15 | |
| dc.date.accessioned | 2026-07-07T05:22:23Z | |
| dc.date.available | 2026-07-07T05:22:23Z | |
| dc.description | 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). | |
| dc.description | 24 pages | |
| dc.identifier | https://arxiv.org/abs/math/0508265 | |
| dc.identifier | http://arxiv.org/abs/math/0508265 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/76042 | |
| dc.subject | Combinatorics | |
| dc.subject | 05C50 | |
| dc.title | Smith Normal Form and Acyclic Matrics | |
| dc.type | text |