Results 11 to 20 of about 16,994 (219)
Domination Number, Independent Domination Number and 2-Independence Number in Trees
Discussiones Mathematicae Graph Theory, 2021 For a graph G, let γ(G) be the domination number, i(G) be the independent domination number and β2(G) be the 2-independence number. In this paper, we prove that for any tree T of order n ≥ 2, 4β2(T) − 3γ(T) ≥ 3i(T), and we characterize all trees ...
Dehgardi Nasrin +4 more
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Medium Domination Decomposition of Graphs
Ratio Mathematica, 2022 A set of vertices in a graph dominates if every vertex in is either in or adjacent to a vertex in . The size of any smallest dominating set is called domination number of .
E Ebin Raja Merly, Saranya J
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Stability of Domination in Graphs
Ratio Mathematica, 2023 The stability of dominating sets in Graphs is introduced and studied, in this paper. Here D is a dominating set of Graph G. In this paper the vertices of D and vertices of $V - D$ are called donors and acceptors respectively.
Reeja Kuriakose, K. S Parvathy
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On domination multisubdivision number of unicyclic graphs [PDF]
Opuscula Mathematica, 2018 The paper continues the interesting study of the domination subdivision number and the domination multisubdivision number. On the basis of the constructive characterization of the trees with the domination subdivision number equal to 3 given in [H. Aram,
Joanna Raczek
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A Note on the Paired-Domination Subdivision Number of Trees
Mathematics, 2021 For a graph G with no isolated vertex, let γpr(G) and sdγpr(G) denote the paired-domination and paired-domination subdivision numbers, respectively. In this note, we show that if T is a tree of order n≥4 different from a healthy spider (subdivided star),
Xiaoli Qiang +5 more
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Graphs with equal domination and independent domination numbers
AKCE International Journal of Graphs and Combinatorics, 2020 Let γ(G) and i(G) denote the domination number and independent domination number of a graph G. In this article, we establish a sufficient condition for a graph G to satisfy which yields some of the well known classical theorems as corollaries.
Purnima Gupta, Rajesh Singh, S. Arumugam
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Characterization of outerplanar graphs with equal 2-domination and domination numbers
Theory and Applications of Graphs, 2022 A {\em $k$-domination number} of a graph $G$ is minimum cardinality of a $k$-dominating set of $G$, where a subset $S \subseteq V(G)$ is a {\em $k$-dominating set} if each vertex $v\in V(G)\setminus S$ is adjacent to at least $k$ vertices in $S$.
Naoki Matsumoto
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On the Paired-Domination Subdivision Number of Trees
Mathematics, 2021 A paired-dominating set of a graph G without isolated vertices is a dominating set of vertices whose induced subgraph has perfect matching. The minimum cardinality of a paired-dominating set of G is called the paired-domination number γpr(G) of G.
Shouliu Wei +4 more
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On the edge geodetic and edge geodetic domination numbers of a graph [PDF]
Communications in Combinatorics and Optimization, 2020 In this paper, we study both concepts of geodetic dominating and edge geodetic dominating sets and derive some tight upper bounds on the edge geodetic and the edge geodetic domination numbers.
Vladimir Samodivkin
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The paired-domination and the upper paired-domination numbers of graphs [PDF]
Opuscula Mathematica, 2015 In this paper we continue the study of paired-domination in graphs. A paired-dominating set, abbreviated PDS, of a graph \(G\) with no isolated vertex is a dominating set of vertices whose induced subgraph has a perfect matching.
Włodzimierz Ulatowski
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