Weighted graphs: Eigenvalues and chromatic number - Charles Delorme (GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB, 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 m+22 vertices.