The critical group of a directed graph
| dc.creator | Wagner, David G. | |
| dc.date | 2000-10-25 | |
| dc.date.accessioned | 2026-07-07T04:38:15Z | |
| dc.date.available | 2026-07-07T04:38:15Z | |
| dc.description | The critical group K(G) of a directed graph G=(V,E) is the cokernel of the transpose of the Laplacian matrix of G acting on the integer lattice Z^V. For undirected graphs G, this has been considered by Bacher, de la Harpe, and Nagnibeda, and by Biggs. We prove several things, among which are: K(G/p) is a subgroup of K(G) when p is an equitable partition and G is strongly connected; for undirected graphs, the torsion subgroup of K(G) depends only on the graphic matroid of G; and, the `dollar game' of Biggs can be generalized to give a combinatorial interpretation for the elements of K(G), when G is strongly connected. | |
| dc.description | 23 pages | |
| dc.identifier | https://arxiv.org/abs/math/0010241 | |
| dc.identifier | http://arxiv.org/abs/math/0010241 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/60202 | |
| dc.subject | Combinatorics | |
| dc.subject | Rings and Algebras | |
| dc.subject | 05C30, 05C25 | |
| dc.title | The critical group of a directed graph | |
| dc.type | text |