Constructing cospectral signed graphs

A well-known fact in Spectral Graph Theory is the existence of pairs of cospectral (or isospectral) nonisomorphic graphs, known as PINGS. The work of A.J. Schwenk (in 1973) and of C. Godsil and B. McKay (in 1982) shed some light on the explanation of the presence of cospectral graphs, and they gave routines to construct PINGS. Here, we consider the Godsil–McKay-type routines developed for graphs, whose adjacency matrices are (Formula presented.) -matrices, to the level of signed graphs, whose adjacency matrices allow the presence of (Formula presented.) s. We show that, with suitable adaption, such routines can be successfully ported to signed graphs, and we can build pairs of cospectral switching nonisomorphic signed graphs.