The eigenvalues of a signed graph are the eigenvalues of its adjacency matrix. In this paper, we consider the problem of identifying the signed graphs with a small number of positive eigenvalues. We characterize the complete signed graphs having exactly two positive eigenvalues. In addition, we completely characterize the complete bipartite signed graphs having exactly three positive eigenvalues.
On signed graphs with at most three positive eigenvalues / Wang, Y.; Belardo, F.; Li, D.. - In: LINEAR ALGEBRA AND ITS APPLICATIONS. - ISSN 0024-3795. - 729:(2026), pp. 293-307. [10.1016/j.laa.2025.10.005]
On signed graphs with at most three positive eigenvalues
Belardo F.;
2026
Abstract
The eigenvalues of a signed graph are the eigenvalues of its adjacency matrix. In this paper, we consider the problem of identifying the signed graphs with a small number of positive eigenvalues. We characterize the complete signed graphs having exactly two positive eigenvalues. In addition, we completely characterize the complete bipartite signed graphs having exactly three positive eigenvalues.File in questo prodotto:
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