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Total Domination Multisubdivision Number of a Graph [PDF]
Discussiones Mathematicae Graph Theory, 2015 The domination multisubdivision number of a nonempty graph G was defined in [3] as the minimum positive integer k such that there exists an edge which must be subdivided k times to increase the domination number of G.
Avella-Alaminos Diana +3 more
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Bounds on the Locating-Domination Number and Differentiating-Total Domination Number in Trees [PDF]
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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Total and Double Total Domination Number on Hexagonal Grid [PDF]
Mathematics, 2019 In this paper, we determine the upper and lower bound for the total domination number and exact values and the upper bound for the double-total domination number on hexagonal grid H m , n with m hexagons in a row and n hexagons in a column ...
Antoaneta Klobučar, Ana Klobučar
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Graphs with large disjunctive total domination number [PDF]
Discrete Mathematics & Theoretical Computer Science, 2015 Graph ...
Michael A. Henning, Viroshan Naicker
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3-Tuple Total Domination Number of Rook’s Graphs
Discussiones Mathematicae Graph Theory, 2022 A k-tuple total dominating set (kTDS) of a graph G is a set S of vertices in which every vertex in G is adjacent to at least k vertices in S. The minimum size of a kTDS is called the k-tuple total dominating number and it is denoted by γ×k,t(G).
Pahlavsay Behnaz +2 more
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Properties of the Global Total k-Domination Number
Mathematics, 2021 A nonempty subset D⊂V of vertices of a graph G=(V,E) is a dominating set if every vertex of this graph is adjacent to at least one vertex from this set except the vertices which belong to this set itself.
Frank A. Hernández Mira +3 more
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A note on bipartite graphs whose [1,k]-domination number equal to their number of vertices [PDF]
Opuscula Mathematica, 2020 A subset \(D\) of the vertex set \(V\) of a graph \(G\) is called an \([1,k]\)-dominating set if every vertex from \(V-D\) is adjacent to at least one vertex and at most \(k\) vertices of \(D\).
Narges Ghareghani +2 more
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On a conjecture concerning total domination subdivision number in graphs
AKCE International Journal of Graphs and Combinatorics, 2021 Let be the total domination number and let be the total domination subdivision number of a graph G with no isolated vertex. In this paper, we show that for some classes of graphs G, which partially solve the conjecture presented by Favaron et al.
S. Kosari +5 more
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Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2015 Let G = (V;E) be a graph. A set S ⊂ V (G) is a hop dominating set of G if for every v ∈ V - S, there exists u ∈ S such that d(u; v) = 2. The minimum cardinality of a hop dominating set of G is called a hop domination number of G and is denoted by γh(G ...
Natarajan C., Ayyaswamy S.K.
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Total domination game on ladder graphs [PDF]
Songklanakarin Journal of Science and Technology (SJST), 2021 The total domination game is played on a simple graph G by two players, named Dominator and Staller. They alternately select a vertex of G; each chosen vertex totally dominates its neighbors.
Karnchana Charoensitthichai +1 more
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