منابع مشابه
Domination game critical graphs
17 The domination game is played on a graph G by two players who alternately take 18 turns by choosing a vertex such that in each turn at least one previously undominated 19 vertex is dominated. The game is over when each vertex becomes dominated. One 20 of the players, namely Dominator, wants to finish the game as soon as possible, while 21 the other one wants to delay the end. The number of t...
متن کاملPaired-Domination Game Played in Graphs
In this paper, we continue the study of the domination game in graphs introduced by Bre{v{s}}ar, Klav{v{z}}ar, and Rall. We study the paired-domination version of the domination game which adds a matching dimension to the game. This game is played on a graph $G$ by two players, named Dominator and Pairer. They alternately take turns choosing vertices of $G$ such that each vertex chosen by Domin...
متن کاملDomination dot-critical graphs
A graph G is dot-critical if contracting any edge decreases the domination number. It is totally dot-critical if identifying any two vertices decreases the domination number. We show that the totally dot-critical graphs essentially include the much-studied domination vertex-critical and edge-critical graphs as special cases. We investigate these properties, and provide a characterization of dot...
متن کاملDistance domination-critical graphs
A set D of vertices in a connected graph G is called a k-dominating set if every vertex in G − D is within distance k from some vertex of D. The k-domination number of G, γk(G), is the minimum cardinality over all k-dominating sets of G. A graph G is k-distance domination-critical if γk(G − x) < γk(G) for any vertex x in G. This work considers properties of k-distance domination-critical graphs...
متن کاملNonsplit Domination Edge Critical Graphs
A set of vertices S is said to dominate the graph G if for each v / ∈ S, there is a vertex u ∈ S with u adjacent to v. The minimum cardinality of any dominating set is called the domination number of the graph G and is denoted by γ(G). A dominating set D of a graph G = (V,E) is a nonsplit dominating set if the induced graph 〈V − D〉 is connected. The nonsplit domination number γns(G) of the grap...
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ژورنال
عنوان ژورنال: Discussiones Mathematicae Graph Theory
سال: 2015
ISSN: 1234-3099,2083-5892
DOI: 10.7151/dmgt.1839