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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.
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https://hal.archives-ouvertes.fr/hal-00360279
Contributor : Lucas Vienne Connect in order to contact the contributor
Submitted on : Wednesday, February 11, 2009 - 9:03:59 AM
Last modification on : Wednesday, October 20, 2021 - 3:18:45 AM
Long-term archiving on: : Tuesday, June 8, 2010 - 10:11:51 PM

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

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Lucas Vienne. Représentations linéaires des graphes finis. 2009. ⟨hal-00360279⟩

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