Représentations linéaires des graphes finis

Abstract : 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.
Liste complète des métadonnées
Contributeur : Lucas Vienne <>
Soumis le : mercredi 11 février 2009 - 09:03:59
Dernière modification le : mercredi 19 décembre 2018 - 14:08:04
Document(s) archivé(s) le : mardi 8 juin 2010 - 22:11:51


  • HAL Id : hal-00360279, version 1
  • ARXIV : 0902.1874



Lucas Vienne. Représentations linéaires des graphes finis. 12 pages. 2009. 〈hal-00360279〉



Consultations de la notice


Téléchargements de fichiers