Weakly connected domination stable trees
نویسندگان
چکیده
منابع مشابه
Weakly connected domination subdivision numbers
A set D of vertices in a graph G = (V, E) is a weakly connected dominating set of G if D is dominating in G and the subgraph weakly induced by D is connected. The weakly connected domination number of G is the minimum cardinality of a weakly connected dominating set of G. The weakly connected domination subdivision number of a connected graph G is the minimum number of edges that must be subdiv...
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The weakly connected domination subdivision number sdγw(G) of a connected graph G is the minimum number of edges which must be subdivided (where each edge can be subdivided at most once) in order to increase the weakly connected domination number. The graph is strongγw-subdivisible if for each edge uv ∈ E(G) we have γw(Guv) > γw(G), where Guv is a graph G with subdivided edge uv. The graph is s...
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Let G = (V,E) be a connected undirected graph. For any vertex v ∈ V , the closed neighborhood of v is N [v] = {v} ∪ {u ∈ V | uv ∈ E }. For S ⊆ V , the closed neighborhood of S is N [S] = ⋃ v∈S N [v]. The subgraph weakly induced by S is 〈S〉w = (N [S], E ∩ (S × N [S])). A set S is a weakly-connected dominating set of G if S is dominating and 〈S〉w is connected. The weakly-connected domination numb...
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Let G = (V, E) be a graph. Set D ⊆ V (G) is a total outerconnected dominating set of G if D is a total dominating set in G and G[V (G)−D] is connected. The total outer-connected domination number of G, denoted by γtc(G), is the smallest cardinality of a total outer-connected dominating set of G. We show that if T is a tree of order n, then γtc(T ) ≥ d 2n 3 e. Moreover, we constructively charact...
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ژورنال
عنوان ژورنال: Czechoslovak Mathematical Journal
سال: 2009
ISSN: 0011-4642,1572-9141
DOI: 10.1007/s10587-009-0007-5