3 A function f : V (G) → {+1,−1} defined on the vertices of a graph G is a signed domi4 nating function if for any vertex v the sum of function values over its closed neighborhood 5 is at least one. The signed domination number γs(G) of G is the minimum weight of a 6 signed dominating function on G. By simply changing “{+1,−1}” in the above definition 7 to “{+1, 0,−1}”, we can define the minus ...

Let G = (V, E) be a simple graph with vertex set V and edge set E. A function f from V to a set {-1, 1} is said to be a nonnegative signed dominating function (NNSDF) if the sum of its function values over any closed neighborhood is at least zero. The weight of f is the sum of function values of vertices in V. The nonnegative signed domination number for a graph G equals the minimum weight of a...

A signed dominating function of a graph G with vertex set V is a function f : V → {−1, 1} such that for every vertex v in V the sum of the values of f at v and at every vertex u adjacent to v is at least 1. The weight of f is the sum of the values of f at every vertex of V . The signed domination number of G is the minimum weight of a signed dominating function of G. In this paper, we study the...

This paper is motivated by the concept of the signed k-domination problem and dedicated to the complexity of the problem on graphs. For any fixed nonnegative integer k, we show that the signed k-domination problem is NP-complete for doubly chordal graphs. For strongly chordal graphs and distance-hereditary graphs, we show that the signed k-domination problem can be solved in polynomial time. We...