Unbalanced Unicyclic and Bicyclic Graphs with Extremal Spectral Radius

A signed graph Γ is a graph whose edges are labeled by signs. If Γ has n vertices, its spectral radius is the number ϱ(Γ):= max{∣λi(Γ)∣: 1 ⩽ i ⩽ n}, where λ1(Γ) ⩾ ⋯ ⩾ λn(Γ) are the eigenvalues of the signed adjacency matrix A(Γ). Here we determine the signed graphs achieving the minimal or the maximal spectral radius in the classes Un and Bn of unbalanced unicyclic graphs and unbalanced bicyclic graphs, respectively.