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 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...
متن کاملMajority domination vertex critical graphs
This paper deals the graphs for which the removal of any vertex changes the majority domination number of the graph. In the following section, how the removal of a single vertex fromG can change the majority domination number is surveyed for trees. Characterisation of V + M (G) and V − M (G) are determined.
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series B
سال: 1983
ISSN: 0095-8956
DOI: 10.1016/0095-8956(83)90007-2