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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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Maker-Breaker domination number [PDF]
Bulletin of the Malaysian Mathematical Sciences Society, 2019 The Maker-Breaker domination game is played on a graph $G$ by Dominator and Staller. The players alternatively select a vertex of $G$ that was not yet chosen in the course of the game.
Gledel, Valentin +2 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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Independent [1,2]-number versus independent domination number [PDF]
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2017 A [1; 2]-set S in a graph G is a vertex subset such that every vertex not in S has at least one and at most two neighbors in it. If the additional requirement that the set be independent is added, the existence of such sets is not guaranteed in every ...
Aleid Sahar A. +2 more
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On the equality of domination number and 2-domination number
Discussiones Mathematicae Graph TheoryThe 2-domination number $ _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, $ _2(G) $ cannot be smaller than the domination number $ (G) $. We consider a large class of graphs and characterize those members which satisfy $ _2=
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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Trees with paired-domination number twice their domination number [PDF]
, 2006 Henning, Michael A. +1 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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