Tight bounds on the chromatic sum of a connected graph
Carsten Thomassen, P. Erdös, Yousef Alavi, Paresh J. Malde, Allen J. Schwenk · Journal of Graph Theory · 1989
Abstract The chromatic sum of a graph is introduced in the dissertation of Ewa Kubicka. It is the smallest possible total among all proper colorings of G using natural numbers. In this article we determine tight bounds on the chromatic sum of a connected graph with e edges.