On signed total domination concept of generalized graphs and networks

Let G=(V,E) be a graph. The function f:V(G)→{-1,1} is a signed total domination function if for all vertices v∈V(G), ∑_(x∈N_G (v))〖f(x)≥1〗, where N_G (v) is the open neighborhood of vertex v. The minimum of values of ω(f)= ∑_(x∈V(G))〖f(x)〗 is called signed total domination number and denoted by γ_st (G) The signed total domination concept is an lp integer programming and NP-hardness problem. In this paper, we initiate studying of signed total domination number for generalized graphs and networks.