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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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On the equality of domination number and 2-domination number [PDF]
Discussiones Mathematicae Graph Theory, 2019 The 2-domination number γ2(G) of a graph G is the minimum cardinality of a set D ⊆ V (G) for which every vertex outside D is adjacent to at least two vertices in D. Clearly, γ2(G) cannot be smaller than the domination number γ(G).
Gülnaz Boruzanlı Ekinci +1 more
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Maker–Breaker Domination Number [PDF]
Bulletin of the Malaysian Mathematical Sciences Society, 2018 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.
Valentin Gledel +2 more
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On the 2-domination Number of Cylinders with Small Cycles [PDF]
Fundamenta Informaticae, 2022 Domination-type parameters are difficult to manage in Cartesian product graphs and there is usually no general relationship between the parameter in both factors and in the product graph.
Ester M. Garzón +3 more
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On the Paired-Domination Subdivision Number of a Graph [PDF]
Mathematics, 2021 In order to increase the paired-domination number of a graph G, the minimum number of edges that must be subdivided (where each edge in G can be subdivided no more than once) is called the paired-domination subdivision number sdγpr(G) of G.
Guoliang Hao +4 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 parameters with number
, 2017 In this paper, we study the most basic domination invariants in graphs, in which number 2 is intrinsic part of their definitions. We classify them upon three criteria, two of which give the following previously studied invariants: the weak 2-domination ...
Flavia Bonomo +4 more
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Domination Number of Graphs with Minimum Degree Five [PDF]
Discussiones Mathematicae Graph Theory, 2019 We prove that for every graph G on n vertices and with minimum degree five, the domination number γ(G) cannot exceed n/3. The proof combines an algorithmic approach and the discharging method.
Csilla Bujt'as
semanticscholar +3 more sources
Bounding the locating-total domination number of a tree in terms of its annihilation number
Discussiones Mathematicae Graph Theory, 2018 Suppose G = (V,E) is a graph with no isolated vertex. A subset S of V is called a locating-total dominating set of G if every vertex in V is adjacent to a vertex in S, and for every pair of distinct vertices u and v in V −S, we have N(u) ∩ S ≠ N(v) ∩ S ...
Mei Lu, Wenjie Ning, Kun Wang
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