Results 41 to 50 of about 11,159 (184)
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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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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Total domination subdivision numbers of trees
Discrete Mathematics, 2004 The total domination subdivision number \(\text{ sd}_{\gamma_t}(G)\) of a graph \(G\) is the minimum number of edges whose subdivision increases the total domination number \({\gamma_t}(G)\) of \(G\). \textit{T. W. Haynes} et al. [J. Comb. Math. Comb. Comput.
Haynes, Teresa W. +2 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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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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Total dominator total chromatic numbers of cycles and paths
RAIRO - Operations Research, 2023 The total dominator total coloring of a graph is a total coloring of the graph such that each object (vertex or edge) of the graph is adjacent or incident to every object of some color class. The minimum number of the color classes of a total dominator total coloring of a graph is called the total dominator total chromatic number of the graph. In (A.P.
Kazemi, Adel P., Kazemnejad, Farshad
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On the Secure Total Domination Number of Graphs [PDF]
Symmetry, 2019 A total dominating set D of a graph G is said to be a secure total dominating set if for every vertex u ∈ V ( G ) \ D , there exists a vertex v ∈ D , which is adjacent to u, such that ( D \ { v } ) ∪ { u } is a total dominating set as well.
Abel Cabrera Martínez +2 more
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Total domination and total domination subdivision number of a graph and its complement
Discrete Mathematics, 2008 AbstractA set S of vertices of a graph G=(V,E) with no isolated vertex is a total dominating set if every vertex of V(G) is adjacent to some vertex in S. The total domination number γt(G) is the minimum cardinality of a total dominating set of G. The total domination subdivision number sdγt(G) is the minimum number of edges that must be subdivided in ...
Odile Favaron +2 more
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Results on the domination number and the total domination number of Lucas cubes
Ars Mathematica Contemporanea, 2020 Lucas cubes are special subgraphs of Fibonacci cubes. For small dimensions, their domination numbers are obtained by direct search or integer linear programming. For larger dimensions some bounds on these numbers are given. In this work, we present the exact values of total domination number of small dimensional Lucas cubes and present optimization ...
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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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