Weighted graphs: Eigenvalues and chromatic number

Charles Delorme
2016 Electronic Journal of Graph Theory and Applications  
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 2 m , a 3-chromatic graph on m+2 2 vertices.
doi:10.5614/ejgta.2016.4.1.2 fatcat:67rdunypv5hd3pks3sdsyemary