Représentations linéaires des graphes finis
| dc.creator | Vienne, Lucas | |
| dc.date | 2009-02-11 | |
| dc.date.accessioned | 2026-07-07T12:40:35Z | |
| dc.date.available | 2026-07-07T12:40:35Z | |
| dc.description | Let X be a non-empty finite set and alpha a symmetric bilinear form on a real finite dimensional vector space E. We say that a set GG={U_i | i in X} of linear lines in E is an isometric sheaf, if there exist generators u_i of the lines U_i, and real constants ''omega'' and ''c '' such that : forall i,j in X, alpha(u_i,u_i)=omega, and if i is different from j, then alpha(u_i,u_j)=epsilon_{i,j}.c, with epsilon_i,j in {-1,+1} Let Gamma be the graph whose set of vertices is X, two of them, say i and j, being linked when epsilon_{i,j} = - 1. In this article we explore the relationship between GG and Gamma ; we describe all sheaves associated with a given graph Gamma and construct the group of isometries stabilizing one of those as an extension group of Aut(Gamma). We finally illustrate our construction with some examples. | |
| dc.description | 12 pages | |
| dc.identifier | https://arxiv.org/abs/0902.1874 | |
| dc.identifier | http://arxiv.org/abs/0902.1874 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/219485 | |
| dc.subject | Combinatorics | |
| dc.subject | Group Theory | |
| dc.subject | 05C25; 05C50; 05C62; 20B20; 20B05; 20B25 | |
| dc.title | Représentations linéaires des graphes finis | |
| dc.type | text |