Représentations linéaires des graphes finisReportar como inadecuado

 Représentations linéaires des graphes finis

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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, alphau i,u i=omega, and if i is different from j, then alphau 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 AutGamma. We finally illustrate our construction with some examples.

Autor: Lucas Vienne


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