On signed majority total domination in graphs
Huaming Xing, Liang Sun, Xue-gang Chen · Czechoslovak Mathematical Journal · 2005
We initiate the study of signed majority total domination in graphs. Let G = (V, E) be a simple graph. For any real valued function f: V → ℝ and S $$ \subseteq$$ V, let $$f(S) = \sum\limits_{v \in S} {\;f(v)}$$ . A signed majority total dominating function is a function f: V → {−1, 1} such that f(N(v)) ≥ 1 for at least a half of the vertices v ∈ V. The signed majority total domination number of a graph G is $$\gamma _{maj}^t (G)$$ = min{f(V): f is a signed majority total dominating function on G}. We research some properties of the signed majority total domination number of a graph G and obtain a few lower bounds of $$\gamma _{maj}^t (G)$$ .