The inverse inertia problem for graphs
| dc.creator | Barrett, Wayne | |
| dc.creator | Hall, H. Tracy | |
| dc.creator | Loewy, Raphael | |
| dc.date | 2007-11-20 | |
| dc.date.accessioned | 2026-07-07T08:43:56Z | |
| dc.date.available | 2026-07-07T08:43:56Z | |
| dc.description | Let G be an undirected graph on n vertices and let S(G) be the set of all real symmetric n x n matrices whose nonzero off-diagonal entries occur in exactly the positions corresponding to the edges of G. The inverse inertia problem for G asks which inertias can be attained by a matrix in S(G). We give a complete answer to this question for trees in terms of a new family of graph parameters, the maximal disconnection numbers of a graph. We also give a formula for the inertia set of a graph with a cut vertex in terms of inertia sets of proper subgraphs. Finally, we give an example of a graph that is not inertia-balanced, and investigate restrictions on the inertia set of any graph. | |
| dc.description | 83 pages, 15 figures | |
| dc.identifier | https://arxiv.org/abs/0711.3049 | |
| dc.identifier | http://arxiv.org/abs/0711.3049 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/142491 | |
| dc.subject | Combinatorics | |
| dc.subject | Spectral Theory | |
| dc.subject | 05C05, 05C50 (Primary); 15A03, 15A57 (Secondary) | |
| dc.title | The inverse inertia problem for graphs | |
| dc.type | text |