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MiS Preprint

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.

MSC Codes:
05C22, 05C5
signed graph eigenvalue, star complement, maximal extension, signed line graph

Related publications

2022 Journal Open Access
Raffaella Mulas and Zoran Stanić

Star complements for ±2 in signed graphs

In: Special matrices, 10 (2022) 1, pp. 258-266