Coloring of trees with minimum sum of colors

@article{Jiang1999ColoringOT,
  title={Coloring of trees with minimum sum of colors},
  author={Tao Jiang and Douglas B. West},
  journal={Journal of Graph Theory},
  year={1999},
  volume={32},
  pages={354-358}
}
The chromatic sum Σ(G) of a graph G is the smallest sum of colors among all proper colorings with natural numbers. The strength s(G) of G is the minimum number of colors needed to achieve the chromatic sum. We construct for each positive integer k a tree Tk with strength k that has maximum degree only 2k − 2. The result is best possible.