Edge-local equivalence of graphs
| dc.creator | Nest, Maarten Van den | |
| dc.creator | De Moor, Bart | |
| dc.date | 2005-10-12 | |
| dc.date.accessioned | 2026-07-07T06:47:24Z | |
| dc.date.available | 2026-07-07T06:47:24Z | |
| dc.description | The local complement G*i of a simple graph G at one of its vertices i is obtained by complementing the subgraph induced by the neighborhood of i and leaving the rest of the graph unchanged. If e={i,j} is an edge of G then G*e=((G*i)*j)*i is called the edge-local complement of G along the edge e. We call two graphs edge-locally equivalent if they are related by a sequence of edge-local complementations. The main result of this paper is an algebraic description of edge-local equivalence of graphs in terms of linear fractional transformations of adjacency matrices. Applications of this result include (i) a polynomial algorithm to recognize whether two graphs are edge-locally equivalent, (ii) a formula to count the number of graphs in a class of edge-local equivalence, and (iii) a result concerning the coefficients of the interlace polynomial, where we show that these coefficients are all even for a class of graphs; this class contains, as a subset, all strongly regular graphs with parameters (n, k, a, c), where k is odd and a and c are even. | |
| dc.description | 25 pages, 2 figures | |
| dc.identifier | https://arxiv.org/abs/math/0510246 | |
| dc.identifier | http://arxiv.org/abs/math/0510246 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/103640 | |
| dc.subject | Combinatorics | |
| dc.subject | Quantum Physics | |
| dc.title | Edge-local equivalence of graphs | |
| dc.type | text |