Résumé | From Alon-Boppana and Serre, we know that for any given integer $kgeq 3$ and real number $lambda<2sqrt{k-1}$, there are finitely many $k$-regular graphs whose second largest eigenvalue is at most $lambda$. In this talk, I will discuss the largest number of vertices in such graphs. This is joint work with Hiroshi Nozaki (Aichi Univ. of Education, Japan), Jack Koolen (Univ. of Science and Technology of China) and Jason Vermette (Missouri Baptist Univ., USA). |