Geodesic
Notes on exceptional signed graphs
Ars Mathematica Contemporanea, Tome 18 (2020) no. 1, pp. 105-115.

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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.
DOI : 10.26493/1855-3974.1933.2df
Keywords: Adjacency matrix, least eigenvalue, root system, signed line graph, exceptional signed graph, signed graph decomposition 
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Zoran Stanić. Notes on exceptional signed graphs. Ars Mathematica Contemporanea, Tome 18 (2020) no. 1, pp. 105-115. doi : 10.26493/1855-3974.1933.2df. http://geodesic.mathdoc.fr/articles/10.26493/1855-3974.1933.2df/

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