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Star complements for ±2 in signed graphs
Raffaella Mulas and Zoran Stanić
In this article, we investigate connected signed graphs which have a connected star complement for both −2 and 2 (i.e. simultaneously for the two eigenvalues), where −2 (resp. 2) is the least (largest) eigenvalue of the adjacency matrix of a signed graph under consideration. We determine all such star complements and their maximal extensions (again, relative to both eigenvalues). As an application, we provide a new proof of the result which identifies all signed graphs that have no eigenvalues other than −2 and 2.