Given a graph, we can calculate the graph norm, which is defined as the largest eigenvalue of the adjacency matrix. Motivated by questions in the study of quantum symmetries, it's interesting to know whether the square of this graph norm is a cyclotomicity integer --- that is, a number which can be written as a sum of several roots in unity. Recent work of Calegari-Guo provides good tools for deciding this question in many examples. This project would require learning the number theory and graph theory background, understanding their technique, and applying it (ideally by writing some computer programs!) to examples.