Sharif Digital Repository

A signed graph is a pair like (G; ), where G is the underlying graph and : E(G) ! f1; +1g is a sign function on the edges of G. Here, we study the spectral determination problem for signed n-cycles (Cn; ) with respect to the adjacency spectrum and the Laplacian spectrum. In particular we prove that signed odd cycles and unbalanced even cycles are uniquely determined by their Laplacian spectrums, but balanced even cycles are not, and we find all L-cospectral mates for them. Moreover, signed odd cycles are uniquely determined by their spectrums but the signed even cycles, (except (C4;) and (C4; +)), are not and we find almost all cospectral mates for them. A mixed graph is obtained from a...