Notes on exceptional signed graphs

Zoran Stanić

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

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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