Spectral Determination of Signed Graphs

TheSpectralDeterminationProblemisoneoftheoldestproblemsinSpectral Graph Theory: given a graph, or a class of graphs, are there non-isomorphic graphs whose spectrum, with respect to a given graph matrix (adjacency, Laplacian, etc.), is the same? The literature contains many results on simple graphs. Here, we focus our attention to Signed Graphs, i.e., graphs whose edges get a sign (say, +1 or−1). The spectral determination problem can be considered for signed graphs as well. We will survey some recent results in this respect.