On the signed total domatic number of a graph

In this paper, we define the signed total domatic number of a graph in an analogous way to that of the fractional domatic number defined by Rail (A fractional version of domatic number. Congr. Numer. 74 (1990), 100-106). A function f: V(G) → {-1, 1} defined on the vertices of a graph G is a signed total dominating function if the sum of its function values over any open neighborhood is at least one. A set {f₁, f_d} of signed total dominating functions on G such that ∑_i=1^d fi(v) ≤ 1 for each vertex v ∈ V(G) is called a signed total dominating family of functions on G. The signed total domatic number of G is the maximum number of functions in a signed total dominating family of G. In this paper we investigate the signed total domatic number for special classes of graphs.