Representation of signed graphs by root system \(E_ 8\)
type: Item
instance of: scholarly article
title: Representation of signed graphs by root system \(E_ 8\)
zbMATH Open document ID: 0821.05040
DOI: 10.1007/BF02986689
author: G. R. Vijayakumar
published in: Graphs and Combinatorics
publication date: 1995-02-01T00:00:00Z
review text: 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.
reviewed by: Dragoš Cvetković
Mathematics Subject Classification ID: 05C50
zbMATH DE Number: 716421
zbMATH Keywords: adjacency matrix
zbMATH Keywords: sigraph
zbMATH Keywords: Gram matrix
zbMATH Keywords: root system
zbMATH Keywords: minimal forbidden sigraphs
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf02986689
OpenAlex ID: W1972448352
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description: scientific article; zbMATH DE number 716421