2009/02/11 by Lucas Vienne, Vienne, Lucas
Computer Science · Mathematics · #05C25 #05C50 #05C62 #20B05 #20B20 #20B25 #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Group Theory (math.GR) #math.CO #math.GR #msc:05C25 #msc:05C50 #msc:05C62 #msc:20B05 #msc:20B20 #msc:20B25
paper · pdf · doi:10.48550/arxiv.0902.1874
12 pages
arxiv created 2009/02/11 · openalex publication_date 2009/02/11 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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=Ui | i in X of linear lines in E is an isometric sheaf, if there exist generators ui of the lines Ui, and real constants ''omega'' and ''c '' such that : forall i,j in X, alpha(ui,ui)=omega, and if i is different from j, then alpha(ui,uj)=epsiloni,j.c, with epsiloni,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 epsiloni,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.