2021/05/18 by Hans Cuypers, Cuypers, Hans
Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #math.CO
paper · pdf · doi:10.48550/arxiv.2105.08618
arxiv created 2021/05/18 · arxiv updated 2021/05/19
The line graph Γ of a multi-graph Δ is the graph whose vertices are the edges of Δ, where two such edges are adjacent if and only if they meet in a single vertex of Δ. We provide several characterizations of such line graphs and in particular show that a graph is a line graph if and only if it does not contain one of 33 graphs, all of which correspond to bases of anisotropic vectors of a 6-dimensional orthogonal geometry of --type over a field with two elements, or, equivalently, to sets of 6 generating reflections in the Weyl group of type E6.