Weighted graphs: Eigenvalues and chromatic number - Charles Delorme (Electronic Journal of Graph Theory and Applications (EJGTA), 2016)
We revisit Hoffman relation involving chromatic number $χ$ and eigenvalues. We construct some graphs and weighted graphs such that the largest and smallest eigenvalues $λ$ dan $μ$ satisfy $λ=(1-χ)μ.$ We study in particular the eigenvalues of the integer simplex $T_m^2,$ a 3-chromatic graph on $\binom {m+2}{2}$ vertices.