Chromatic weak domatic partition in graphs

Abstract

In a simple graph G, a subset D of V (G) is called a chromatic weak dominating set if D is a weak dominating set and χ(< D >) = χ(G). Similar to domatic partition, chromatic weak domatic partition can be defined. The maximum cardinality of a chromatic weak domatic partition is called the chromatic weak domatic number of G. Bounds for this number are obtained and new results are derived involving chromatic weak domatic number and chromatic weak domination number.