Spectral determination of signed graphs

A signed graph is pair (G,s) where G is a graph and s, the signature, is a function on the edges of G assigning values in {1,-1}. Similarly to simple unsigned graphs, it is possible to associate several graph matrices and to study the signed graphs from a spectral viewpoint. A common problem in Spectral Theory of unsigned graphs is to consider special families of graphs and to study whether each graph in the family is determined by the spectrum of the corresponding graph matrix. Namely, a graph is determined by the spectrum if and only if any other cospectral graph is isomorphic as well. In this seminar we extend the latter concept to signed graphs and as an example we will show that the signed Lollipop graph is determined by the spectrum of its Laplacian matrix.

This is a joint research with Pawel Petecki.