On the eigenvalues of complete bipartite signed graphs (Q6650516)

In the main result (Theorem 3.1), the authors determine the lower bound for the nullity of a complete bipartite signed graph, based on the number of end vertices of all negative edges in each part. This result is further extended to a full description of the spectrum of a complete bipartite signed graph in the cases when negative edges induce either a disjoint union of smaller complete bipartite subgraphs (Theorems 4.1, 4.3) or a path (Theorem 4.6). When negative edges induce a regular subgraph, a lower bound on the nullity is again obtained and the spectrum of a complete bipartite signed graph is almost completely described (Theorem 5.2).