Maximal signed graphs with odd signed cycles as star complements

Maximal signed graphs with signed cycles C-3 or C-5 as a star complement for (adjacency) eigenvalue -2 are completely characterized in this paper. The switching equivalence of the maximal signed graphs is studied. Specifically, if Sigma(1)' is switching equivalent to Sigma(2)', and Sigma(1) is a maximal signed graph with Sigma(1)' as a star complement for mu, then there exists a maximal signed graph Sigma(2) switching equivalent to Sigma(1) with Sigma(2)' as a star complement for mu. We also consider the order of the maximal signed graphs with odd cycle as a star complement for eigenvalue -2. (C) 2021 Elsevier Inc. All rights reserved.