New Arithmetic Invariants for Cospectral Graphs

An invariant for cospectral graphs is a property shared by all graphs. In this talk, we give three new invariants for cospectral graphs, characterized by their arithmetic nature. Based on these, we are able to show that under certain conditions, every graph cospectral with a graph $G$ is determined by its generalized spectrum. This is a joint work with Yizhe Ji, Quanyu Tang and Hao Zhang.