# Discrete Seminar: Can you hear the shape of a tree?

**Author: Lona** | Image: Lona

**Author: Lona** | Image: Lona

Speaker: Joel Jeffries, Iowa State University Abstract: Spectral graph theory gives a way to study graph structures by considering the eigenvalues of a matrix derived from a graph. Many questions ask something like “Given a set of eigenvalues associated with a graph, what properties can be recovered about the graph?” We ask if the property “is a tree” can be recovered for several matrices, namely the adjacency, the Laplacian, the signless Laplacian, and the normalized adjacency. In addition, we dive into a problem on the construction of cospectral pairs that arises while answering this question.