Average distances and distance domination numbers
نویسندگان
چکیده
منابع مشابه
Graphs with equal domination and 2-distance domination numbers
Let G = (V,E) be a graph. The distance between two vertices u and v in a connected graph G is the length of the shortest (u−v) path in G. A set D ⊆ V (G) is a dominating set if every vertex of G is at distance at most 1 from an element of D. The domination number of G is the minimum cardinality of a dominating set of G. A set D ⊆ V (G) is a 2-distance dominating set if every vertex of G is at d...
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In this paper, we study a generalization of the paired domination number. Let G= (V ,E) be a graph without an isolated vertex. A set D ⊆ V (G) is a k-distance paired dominating set of G if D is a k-distance dominating set of G and the induced subgraph 〈D〉 has a perfect matching. The k-distance paired domination number p(G) is the cardinality of a smallest k-distance paired dominating set of G. ...
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Let k be a positive integer, and let G be a simple graph with vertex set V (G). A k-distance Roman dominating function on G is a labeling f : V (G) → {0, 1, 2} such that for every vertex with label 0, there is a vertex with label 2 at distance at most k from each other. The weight of a k-distance Roman dominating function f is the value ω(f) = ∑ v∈V f(v). The k-distance Roman domination number ...
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Let k be a positive integer and G = (V,E) be a connected graph of order n. A set D ⊆ V is called a k-dominating set of G if each x ∈ V (G) − D is within distance k from some vertex of D. A connected k-dominating set is a k-dominating set that induces a connected subgraph of G. The connected k-domination number of G, denoted by γ k(G), is the minimum cardinality of a connected k-dominating set. ...
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Theaverage lower independencenumber iav(G)of a graphG=(V ,E) is defined as 1 |V | ∑ v∈V iv(G), and the average lower domination number av(G) is defined as 1 |V | ∑ v∈V v(G), where iv(G) (resp. v(G)) is the minimum cardinality of a maximal independent set (resp. dominating set) that contains v.We give an upper bound of iav(G) and av(G) for arbitrary graphs. Then we characterize the graphs achiev...
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ژورنال
عنوان ژورنال: Discrete Applied Mathematics
سال: 2009
ISSN: 0166-218X
DOI: 10.1016/j.dam.2008.03.024