On signed graphs whose second largest Laplacian eigenvalue does not exceed 3

Let Γ=(G,σ) be a signed graph, where G is the underlying graph and σ:E(G)→{+,-} is the signature function on the edges of G. In this paper, we consider the Laplacian eigenvalues of signed graphs and we characterize the connected signed graphs whose second largest Laplacian eigenvalue does not exceed 3. Furthermore, we study the Laplacian spectral determination of most graphs in the latter family