Displaying similar documents to “Relationships between distance domination parameters.”

Distance in graphs

Roger C. Entringer, Douglas E. Jackson, D. A. Snyder (1976)

Czechoslovak Mathematical Journal

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Vertices Contained In All Or In No Minimum Semitotal Dominating Set Of A Tree

Michael A. Henning, Alister J. Marcon (2016)

Discussiones Mathematicae Graph Theory

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Let G be a graph with no isolated vertex. In this paper, we study a parameter that is squeezed between arguably the two most important domination parameters; namely, the domination number, γ(G), and the total domination number, γt(G). A set S of vertices in a graph G is a semitotal dominating set of G if it is a dominating set of G and every vertex in S is within distance 2 of another vertex of S. The semitotal domination number, γt2(G), is the minimum cardinality of a semitotal dominating...

One-two descriptor of graphs

K. CH. Das, I. Gutman, D. Vukičević (2011)

Bulletin, Classe des Sciences Mathématiques et Naturelles, Sciences mathématiques

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The Distance Roman Domination Numbers of Graphs

Hamideh Aram, Sepideh Norouzian, Seyed Mahmoud Sheikholeslami (2013)

Discussiones Mathematicae Graph Theory

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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 w(f) =∑v∈V f(v). The k-distance Roman domination number of a graph G, denoted by γkR (D), equals the minimum weight of a k-distance Roman dominating...