Regular Graphs of Degree at most Four that Allow Two Distinct Eigenvalues

Wayne Barrett, Shaun Fallat, Veronika Furst +3

For an $n\times n$ matrix $A$, let $q(A)$ be the number of distinct eigenvalues of $A$. If $G$ is a connected graph on $n$ vertices, let $\mathcal{S}(G)$ be the set of all real sy…