Abstract
Maximal signed graphs with signed cycles C3 or C5 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 Σ1′ is switching equivalent to Σ2′, and Σ1 is a maximal signed graph with Σ1′ as a star complement for μ, then there exists a maximal signed graph Σ2 switching equivalent to Σ1 with Σ2′ as a star complement for μ. We also consider the order of the maximal signed graphs with odd cycle as a star complement for eigenvalue −2.
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