A k-dominating set is a set D k V such that every vertex i 2 V nD k has at least k i neighbours in D k. The k-domination number k (G) of G is the cardinality of a smallest k-dominating set of G. For k 1 = ::: = k n = 1, k-domination corresponds to the usual concept of domination. Our approach yields an improvement of an upper bound for the domination number found then the conception of k-domina...

In this paper, we introduce the closed domination in graphs. Some interesting relationships are known between domination and closed domination and between closed domination and the independent domination. It is also shown that any triple m, k and n of positive integers with 3 ≤ m ≤ k ≤ n are realizable as the domination number, closed domination number and independent domination number, respect...

‎a total dominating set of a graph $g$ is a set $d$ of vertices of $g$ such that every vertex of $g$ has a neighbor in $d$‎. ‎the total domination number of a graph $g$‎, ‎denoted by $gamma_t(g)$‎, ‎is~the minimum cardinality of a total dominating set of $g$‎. ‎chellali and haynes [total and paired-domination numbers of a tree, akce international ournal of graphs and combinatorics 1 (2004)‎, ‎6...

In a probabilistic database, deciding if a tuple u is better than another tuple v has not a univocal solution, rather it depends on the specific probabilistic ranking semantics (PRS) one wants to adopt so as to combine together tuples’ scores and probabilities. In deterministic databases it is known that skyline queries are a remarkable alternative to (top-k) ranking queries, because they remov...

In this paper, we present new upper bounds for the global domination and Roman domination numbers and also prove that these results are asymptotically best possible. Moreover, we give upper bounds for the restrained domination and total restrained domination numbers for large classes of graphs, and show that, for almost all graphs, the restrained domination number is equal to the domination num...