Bojan Mohar: Graphs with many eigenvalues close to their largest eigenvalues
Given $t>0$ and a small $\epsilon>0$, we discuss families of connected $n$-vertex graphs with bounded degrees which have positive proportion of their eigenvalues in an interval $[t-\epsilon,t]$ and only a bounded number of eigenvalues greater than $t$. Special cases when $t=\lambda_1(G)$ or $t=\lambda_2(G)$ are of particular interest because of their relationship to equiangular lines in Euclidean spaces.
Speaker: Bojan Mohar
Simon Fraser University