Weighted graphs: Eigenvalues and chromatic number

We revisit Hoffman relation involving chromatic number (chi) and eigenvalues. We construct some graphs and weighted graphs such that the largest and smallest eigenvalues λ dan µ satisfy λ = (1- (chi) )µ: We study in particular the eigenvalues of the integer simplex T2m ; a 3-chromatic graph on (m+2 2)vertices.