Representation of signed graphs by root system \(E_ 8\)
A graph together with a mapping from the set of edges to the set \(\{1, - 1\}\) is called a sigraph. If \(A\) is the \((1, -1, 0)\)-adjacency matrix of a sigraph, then the matrix \(A+ 2I\) can be interpreted as the Gram matrix of a set of vectors in a real vector space. The author studies sigraphs in which this set of vectors is a subset of the root system \(E_ 8\). The set of minimal forbidden sigraphs for such sigraphs is described. Minimal forbidden sigraphs have at most 10 vertices.
scientific article; zbMATH DE number 716421
scientific article