For a graph with largest normalized Laplacian eigenvalue lambda and (vertex) coloring number chi, it is known that lambda is larger than or equal to chi/(chi-1). We consider properties of graphs for which this bound is sharp, and we study the multiplicity of chi/(chi-1). We also study the spectrum of the 1-sum of two graphs, with a focus on the maximal eigenvalue. Finally, we give upper bounds on lambda in terms of chi.