We study graphs with spectral radius at most $\frac{3}{2}\sqrt{2}$ and refine results by Woo and Neumaier [On graphs whose spectral radius is bounded by $\frac{3}{2}\sqrt{2}$, Graphs Combinatorics 23 (2007), 713-726]. We study the limit points of the spectral radii of certain families of graphs,...

We determine a lower bound for the spectral radius of a graph in terms of the number of vertices and the diameter of the graph. For the specific case of graphs with diameter three we give a slightly better bound. We also construct families of graphs with small spectral radius, thus obtaining...