Notes on exceptional signed graphs

Authors

DOI:

https://doi.org/10.26493/1855-3974.1933.2df

Keywords:

Adjacency matrix, least eigenvalue, root system, signed line graph, exceptional signed graph, signed graph decomposition

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.

Downloads

Published

2020-09-24

Issue

Vol. 18 No. 1 (2020)

Section

Articles

License

Articles in this journal are published under Creative Commons Attribution 4.0 International License
https://creativecommons.org/licenses/by/4.0/