This paper is motivated by the concept of nonnegative signed domination that was introduced by Huang, Li, and Feng in 2013 [15]. We study the non-negative signed domination problem from the theoretical point of view. For networks modeled by strongly chordal graphs and distance-hereditary graphs, we show that the non-negative signed domination problem can be solved in polynomial time. For networ...

Let G = (V, E) a graph. A set D ~ V is a weak dominating set of G if for every vertex y E V D there is a vertex xED with xy E E and d( x, G) ::; d(y, G). The weak domination number rw (G) is defined as the minimum cardinality of a weak dominating set and was introduced by Sampathkumar and Pushpa Latha in [6]. In this paper we present sharp upper bounds on rw(G) for general graphs involving the ...

We provide two algorithms counting the number of minimum Roman dominating functions of a graph on n vertices in (1.5673) n time and polynomial space. We also show that the time complexity can be reduced to (1.5014) n if exponential space is used. Our result is obtained by transforming the Roman domination problem into other combinatorial problems on graphs for which exact algorithms already exist.

Let D be a finite and simple digraph with the vertex set V (D), and let f : V (D) → {−1, 1} be a two-valued function. If∑ x∈N[v] f(x) ≥ 1 for each v ∈ V (D), where N[v] consists of v and all vertices of D from which arcs go into v, then f is a signed dominating function on D. The sum f(V (D)) is called the weight w(f) of f . The minimum of weights w(f), taken over all signed dominating function...

Let G = BHn be a n - dimensional balanced hypercube. As topology of interconnection network, hypercubes are widely used in many areas. The signed k subdomination number graphs is an important parameter the domination theory. In this paper, according to properties hypercubes, (|G| –1) when 2 determined by classified discussion and exhaustived method.