The Signed k-Domination Numbers In Graphs.
Changping Wang · 2012
Abstract. For any integer k ≥ 1, a signed (total) k-dominating function is a function f: V (G) → {−1, 1} satisfying P w∈N[v] f(w) ≥ k (Pw∈N(v) f(w) ≥ k) for every v ∈ V (G), where N(v) = {u ∈ V (G)|uv ∈ E(G)} and N[v] = N(v)∪{v}. The minimum of the values of P v∈V (G) f(v), taken over all signed (total) k-dominating functions f, is called the signed (total) k-domination number and is denoted by γkS(G) (γt kS (G), resp.). In this paper, several sharp lower bounds of these numbers for general graphs are presented. 1.