Delve into the future of research at MiS with our preprint repository. Our scientists are making groundbreaking discoveries and sharing their latest findings before they are published. Explore repository to stay up-to-date on the newest developments and breakthroughs.
MiS Preprint
8/2022
Star complements for ±2 in signed graphs
Raffaella Mulas and Zoran Stanić
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.