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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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Isolation Number versus Domination Number of Trees
Mathematics, 2021 If G=(VG,EG) is a graph of order n, we call S⊆VG an isolating set if the graph induced by VG−NG[S] contains no edges. The minimum cardinality of an isolating set of G is called the isolation number of G, and it is denoted by ι(G).
Magdalena Lemańska +3 more
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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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Domination number of graphs with minimum degree five [PDF]
Discussiones Mathematicae Graph Theory, 2020 We prove that for every graph $G$ on $n$ vertices and with minimum degree five, the domination number $\gamma(G)$ cannot exceed $n/3$. The proof combines an algorithmic approach and the discharging method.
Bujtás, Csilla
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Some results on the super domination number of a graph [PDF]
Discret. Math. Algorithms Appl., 2022 Let $G=(V,E)$ be a simple graph. A dominating set of $G$ is a subset $S\subseteq V$ such that every vertex not in $S$ is adjacent to at least one vertex in $S$.
Nima Ghanbari
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Total domination number of middle graphs [PDF]
Electronic Journal of Graph Theory and Applications, 2022 A total dominating set of a graph G with no isolated vertices is a subset S of the vertex set such that every vertex of G is adjacent to a vertex in S. The total domination number of G is the minimum cardinality of a total dominating set of G.
Farshad Kazemnejad +3 more
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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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The total co-independent domination number of some graph operations
Revista de la Unión Matemática Argentina, 2022 . A set D of vertices of a graph G is a total dominating set if every vertex of G is adjacent to at least one vertex of D . The total domi- nating set D is called a total co-independent dominating set if the subgraph induced by V ( G ) − D is edgeless ...
A. Cabrera Martínez +3 more
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On the outer-independent double Italian domination number
Electronic Journal of Graph Theory and Applications, 2022 An outer-independent Italian dominating function (OIIDF) on a graph G is a function f : V ( G ) −→ { 0 , 1 , 2 } such that every vertex v ∈ V ( G ) with f ( v ) = 0 has at least two neighbors assigned 1 under f or one neighbor w with f ( w ) = 2 , and ...
Noor A'lawiah Abd Aziz +3 more
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