Star complements for ±2 in signed graphs

Raffaella Mulas and Zoran Stanić

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Submission date: 17. Feb. 2022
Bibtex
MSC-Numbers: 05C22, 05C5
Keywords and phrases: signed graph eigenvalue, star complement, maximal extension, signed line graph
Link to arXiv: See the arXiv entry of this preprint.
DOI number (of the published article): 10.1515/spma-2022-0161

Abstract:
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.