At the end of the spectrum: Chromatic bounds for the largest eigenvalue of the normalized Laplacian

Lies Beers, Raffaella Mulas

For a graph with largest normalized Laplacian eigenvalue ${\lambda }_N$ and (vertex) coloring number $\chi$, it is known that ${\lambda }_N\ge \chi /(\chi -1)$. Here we prove properties of graphs for which th…