The independent domatic queen number of a graph Qn is the maximum pairwise disjoint minimum dominating sets Pn and it denoted by id(Qn) while Id(Qn). We discuss about in this paper (maximum independent) on n × chess board.

This paper addresses the problem of the supervised assessment of hierarchical region-based image representations. Given the large amount of partitions represented in such structures, the supervised assessment approaches in the literature are based on selecting a reduced set of representative partitions and evaluating their quality. Assessment results, therefore, depend on the partition selectio...

For a positive integer k, a k-rainbow dominating function of a digraph D is a function f from the vertex set V (D) to the set of all subsets of the set {1, 2, . . . , k} such that for any vertex v ∈ V (D) with f(v) = ∅ the condition u∈N−(v) f(u) = {1, 2, . . . , k} is fulfilled, where N−(v) is the set of in-neighbors of v. A set {f1, f2, . . . , fd} of k-rainbow dominating functions on D with t...

We show that the number of minimal dominating sets in a graph on n vertices is at most 1.7697, thus improving on the trivial O(2n/√n) bound. Our result makes use of the measure and conquer technique from exact algorithms, and can be easily turned into an O(1.7697) listing algorithm. Based on this result, we derive an O(2.8805n) algorithm for the domatic number problem, and an O(1.5780) algorith...

For a positive integer k, a k-rainbow dominating function of a graph G is a function f from the vertex set V (G) to the set of all subsets of the set {1, 2, . . . , k} such that for any vertex v ∈ V (G) with f(v) = ∅ the condition ⋃ u∈N(v) f(u) = {1, 2, . . . , k} is fulfilled, where N(v) is the neighborhood of v. The 1-rainbow domination is the same as the ordinary domination. A set {f1, f2, ....

Let G = (V, E) be a graph. A subset D of V is called common neighbourhood dominating set (CN-dominating set) if for every v ∈ V −D there exists a vertex u ∈ D such that uv ∈ E(G) and |Γ(u, v)| > 1, where |Γ(u, v)| is the number of common neighbourhood between the vertices u and v. The minimum cardinality of such CN-dominating set denoted by γcn(G) and is called common neighbourhood domination n...