Strong-weak domatic numbers of graphs

Let G = (V, E) be a graph and u, v is an element of V. If u v is an element of E and deg ugreater than or equal to deg v, then we say that a strongly dominates v and v weakly dominates u. A subset D of V is called strong dominating set, (sd-set) of G if every vertex in V - D is strongly dominated by, at least one vertex in D. Similarly, a weak dominating set (wd-set) of a graph G is defined. A partition V (G) = V-1 boolean OR V-2 boolean OR...boolean OR V-k is a strong-weak domatic partition (swd-partition) of G if each V-i is a sd-set or a wd-set. The strong-weak domatic number d*(G) of G is the maximum order of a swd-partition of G. In this paper, we investigate the properties of this parameter.