The information boundedness principle for rule based inference process requires that the knowledge obtained as a result of a rule should not have more information than that contained in the consequent of this rule. We formulate the information boundedness principle for aggregation and show that it can be expressed using the notion of dominance. We also investigate conditions under which this pr...

A set D of vertices in a graph G = (V, E) is a dominating set of G if every vertex in V −D is adjacent to some vertex in D. The domination number γ(G) of G is the minimum cardinality of a dominating set. We define the cobondage number bc(G) of G to be the minimum cardinality among the sets of edges X ⊆ P2(V ) −E, where P2(V ) = {X ⊆ V : |X| = 2} such that γ(G + X) < γ(G). In this paper, the exa...

An algorithmic upper bound on the domination number γ of graphs in terms of the order n and the minimum degree δ is proved. It is demonstrated that the bound improves best previous bounds for any 5 ≤ δ ≤ 50. In particular, for δ = 5, Xing et al. proved in 2006 that γ ≤ 5n/14 < 0.3572n. This bound is improved to 0.3440n. For δ = 6, Clark et al. in 1998 established γ < 0.3377n, while Biró et al. ...

In this paper, we provide an upper bound for the k-tuple domination number that generalises known upper bounds for the double and triple domination numbers. We prove that for any graph G, ×k(G) ln( − k + 2)+ ln(∑k−1 m=1(k −m)d̂m + )+ 1 − k + 2 n, where ×k(G) is the k-tuple domination number; is the minimal degree; d̂m is the m-degree of G; = 1 if k = 1 or 2 and =−d if k 3; d is the average degree...

A Roman dominating function on a graph G = (V, E) is a function f : V → {0, 1, 2} satisfying the condition that every vertex u for which f(u) = 0 is adjacent to at least one vertex v for which f(v) = 2. The weight of a Roman dominating function is the value f(V ) = ∑ u∈V f(u). The minimum weight of a Roman dominating function on a graph G is called the Roman domination number of G. In this pape...

We describe various computing techniques for tackling chessboard domination problems and apply these to the determination of domination and irredundance numbers for queens’ and kings’ graphs. In particular we show that γ(Q15) = γ(Q16) = 9, confirm that γ(Q17) = γ(Q18) = 9, show that γ(Q19) = 10, show that i(Q18) = 10, improve the bound for i(Q19) to 10 ≤ i(Q19) ≤ 11, show that ir(Qn) = γ(Qn) fo...

A dominating set S of a graph G is called efficient if |N [v]∩S| = 1 for every vertex v ∈ V (G). That is, a dominating set S is efficient if and only if every vertex is dominated exactly once. In this paper, we investigate efficient multiple domination. There are several types of multiple domination defined in the literature: k-tuple domination, {k}-domination, and k-domination. We investigate ...

For a graph G that models a facility, various detection devices can be placed at the vertices so as to identify the location of an intruder such as a thief or saboteur. Here we introduce the open neighborhood locating-dominating set problem. We seek a minimum cardinality vertex set S with the property that for each vertex v its open neighborhood N(v) has a unique non-empty intersection with S. ...

Ve consider the independence, domination and independent domination numbers of graphs obtained from the moves of queens on chessboards drawn on the torus, and determine exact values for each of these parameters in infinitely many cases.