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 continue the study of the domination game in graphs introduced by Brešar, Klavžar, and Rall [SIAM J. Discrete Math. 24 (2010) 979–991]. We study the total version of the domination game and show that these two versions differ significantly. We present a key lemma, known as the Total Continuation Principle, to compare the Dominator-start total domination game and the Staller-st...

In this paper, we continue the study of neighborhood total domination in graphs first studied by Arumugam and Sivagnanam [Opuscula Math. 31 (2011), 519–531]. A neighborhood total dominating set, abbreviated NTD-set, in a graph G is a dominating set S in G with the property that the subgraph induced by the open neighborhood of the set S has no isolated vertex. The neighborhood total domination n...

Generalized Petersen graphs are an important class of commonly used interconnection networks and have been studied . The total domination number of generalized Petersen graphs P(m,2) is obtained in this paper.