Connected 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 graph G is said to be k-γt-critical if the total domination number γt(G) = k and γt(G + uv) < k for every uv / ∈ E(G). A k-γc-critical graph G is a graph with the connected domination number γc(G) = k and γc(G + uv) < k for every uv / ∈ E(G). Further, a k-tvc graph is a graph with γt(G) = k and γt(G− v) < k for all v ∈ V (G), where v is not a support vertex (i.e. all neighbors of v have degre...
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A dominating set D of a graph G is a subset of V (G) such that for every vertex v ∈ V (G), either v ∈ D or there exists a vertex u ∈ D that is adjacent to v in G. Dominating sets of small cardinality are of interest. A connected dominating set C of a graph G is a dominating set of G such that the subgraph induced by the vertices of C in G is connected. A weakly-connected dominating set W of a g...
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As a generalization of connected domination in a graph G we consider domination by sets having at most k components. The order γ c (G) of such a smallest set we relate to γc(G), the order of a smallest connected dominating set. For a tree T we give bounds on γ c (T ) in terms of minimum valency and diameter. For trees the inequality γ c (T ) ≤ n− k − 1 is known to hold, we determine the class o...
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A subset of vertices D of a graph G is a dominating set for G if every vertex of G not in D is adjacent to one in D. A dominating set for G is a connected dominating set if it induces a connected subgraph of G. The connected domination number of G, denoted by γc(G), is the minimum cardinality of a connected dominating set. Graph G is said to be k−γc−critical if γc(G) = k but γc(G+e) < k for eac...
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ژورنال
عنوان ژورنال: Applied Mathematics Letters
سال: 2004
ISSN: 0893-9659
DOI: 10.1016/s0893-9659(04)90118-8