Notes on exceptional signed graphs
Abstract
A connected signed graph is called exceptional if it has a representation in the root system E8, but has not in any Dk. In this study we obtain some properties of these signed graphs, mostly expressed in terms of those that are maximal with a fixed number of eigenvalues distinct from −2. As an application, we characterize exceptional signed graphs with exactly 2 eigenvalues. In some particular cases, we prove the (non-)existence of such signed graphs.
Keywords
Adjacency matrix, least eigenvalue, root system, signed line graph, exceptional signed graph, signed graph decomposition
DOI: https://doi.org/10.26493/1855-3974.1933.2df
ISSN: 1855-3974
Issues from Vol 6, No 1 onward are partially supported by the Slovenian Research Agency from the Call for co-financing of scientific periodical publications