Signed domatic numbers of the complete bipartite graphs - Volkmann, Lutz (Utilitas Mathematica, 2005)
Let G be a finite and simple graph with vertex set, V(G), and let f: V(G) → -1, 1 be a two-valued function. If Σxε N[v] f (x) ≥ 1 for each vε v(G), where N[v] is the closed neighborhood of v, then f is a signed dominating function on G. A set f1, f2, ..., fd of signed dominating functions on G with the property that Σi=1 d fi(x) ≤ 1 for each x ε V(G), is called a signed dominating family on G. The maximum number of functions in a signed dominating family on G is the signed domatic number on G, denoted by d s(G). In this paper we determine the signed domatic number d s(Kp,q) for all complete bipartite graphs Kp,q.