Matching properties in domination critical graphs
نویسندگان
چکیده
منابع مشابه
Matching properties in connected domination critical graphs
A dominating set of vertices S of a graph G is connected if the subgraph G[S] is connected. Let c(G) denote the size of any smallest connected dominating set in G. A graph G is k-connected-critical if c(G)= k, but if any edge e ∈ E(Ḡ) is added to G, then c(G+ e) k − 1. This is a variation on the earlier concept of criticality of edge addition with respect to ordinary domination where a graph G ...
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A Roman domination function on a graph G is a function r : V (G) → {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 function is the value r(V (G)) = ∑ u∈V (G) r(u). The Roman domination number γR(G) of G is the minimum weight of a Roman domination function on G . "Roman Criticality" has been ...
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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...
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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...
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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...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2004
ISSN: 0012-365X
DOI: 10.1016/s0012-365x(03)00243-7