Results 1 to 10 of about 17,013 (164)
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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Graphs with equal domination and independent domination numbers [PDF]
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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On the equality of domination number and 2-domination number
Discussiones Mathematicae Graph TheoryThe 2-domination number $γ_2(G)$ of a graph $G$ is the minimum cardinality of a set $ D \subseteq V(G) $ for which every vertex outside $ D $ is adjacent to at least two vertices in $ D $. Clearly, $ γ_2(G) $ cannot be smaller than the domination number $ γ(G) $.
Gülnaz Boruzanlı Ekinci +1 more
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Bounds on the Locating-Domination Number and Differentiating-Total Domination Number in Trees
Discussiones Mathematicae Graph Theory, 2018 A subset S of vertices in a graph G = (V,E) is a dominating set of G if every vertex in V − S has a neighbor in S, and is a total dominating set if every vertex in V has a neighbor in S.
Rad Nader Jafari, Rahbani Hadi
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Discussiones Mathematicae Graph Theory, 2014 Let K3n denote the Cartesian product Kn□Kn□Kn, where Kn is the complete graph on n vertices.
Georges John, Lin Jianwei, Mauro David
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The Domination Parameters on a kind of the regular honeycomb structure [PDF]
Computer Science Journal of Moldova, 2022 The honeycomb mesh, based on hexagonal structure, has enormous applications in chemistry and engineering. A major challenge in this field is to understand the unique properties of honeycomb structures, which depend on their properties of topology. One
Fateme Movahedi +2 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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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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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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