图的符号全划分数

Let G = （V, E） be a graph, and let f ： V →{-1, 1} be a two-valued function. If ∑x∈N（v） f（x） ≥ 1 for each v ∈ V, where N（v） is the open neighborhood of v, then f is a signed total dominating function on G. A set {fl, f2,… fd} of signed d total dominating functions on G with the property that ∑i=1^d fi（x） ≤ 1 for each x ∈ V, is called a signed total dominating family （of functions） on G. The maximum number of functions in a signed total dominating family on G is the signed total domatic number on G, denoted by dt^s（G）. The properties of the signed total domatic number dt^s（G） are studied in this paper. In particular, we give the sharp bounds of the signed total domatic number of regular graphs, complete bipartite graphs and complete graphs.

Signed total domatic number of a graph

Let G = (V,E) be a graph, and let f: V →{-1, 1} be a two-valued function. If … f(x)≥1 for each v ∈V,family (of functions) on G. The maximum number of functions in a signed total dominating family on G is the signed totaldomatic number on G, denoted by dθt(G). The properties of the signed total domatic number dst(G) are studied in this paper.In particular, we give the sharp bounds of the signed total domatic number of regular graphs, complete bipartite graphs andcomplete graphs.