The chromatic sum of a graph is the smallest sum of colors among all proper colorings with natural numbers. The strength of a graph is the minimum number of colors necessary to obtain its chromatic sum. A natural generalization of chromatic sum is optimum cost chromatic partition (OCCP) problem, where the costs of colors can be arbitrary positive numbers. Existing results about chromatic sum, strength of a graph, and OCCP problem are presented together with some recent developments. The focus is on polynomial algorithms for some families of graphs and NP-completeness issues. Copyright © 2004 Hindawi Publishing Corporation. All rights reserved.
Kubicka, E. (2004). The chromatic sum of a graph: History and recent developments. International Journal of Mathematics and Mathematical Sciences, 2004(30), 1563–1573. https://doi.org/10.1155/S0161171204306216