Results 21 to 30 of about 13,115 (262)
Trees with equal total domination and game total domination numbers
Discrete Applied Mathematics, 2017 In this paper, we continue the study of the total domination game in graphs introduced in [Graphs Combin. 31(5) (2015), 1453--1462], where the players Dominator and Staller alternately select vertices of $G$. Each vertex chosen must strictly increase the number of vertices totally dominated, where a vertex totally dominates another vertex if they are ...
Michael A. Henning, Douglas F. Rall
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Jambura Journal of Mathematics, 2022 Let G = (V(G), E(G)) be a connected graph, where V(G) is the set of vertices and E(G) is the set of edges. The set Dt(G) is called the total domination set in G if every vertex v 2 V(G) is adjacent to at least one vertex in Dt (G).
Nurhamzah Nurhamzah +2 more
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Total Domination Versus Domination in Cubic Graphs [PDF]
Graphs and Combinatorics, 2017 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Joanna Cyman +4 more
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Total Protection of Lexicographic Product Graphs
Discussiones Mathematicae Graph Theory, 2022 Given a graph G with vertex set V (G), a function f : V (G) → {0, 1, 2} is said to be a total dominating function if Σu∈N(v) f(u) > 0 for every v ∈ V (G), where N(v) denotes the open neighbourhood of v. Let Vi = {x ∈ V (G) : f(x) = i}. A total dominating
Martínez Abel Cabrera +1 more
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Ars Mathematica Contemporanea, 2021 A subset of vertices in a graph is called a total dominating set if every vertex of the graph is adjacent to at least one vertex of this set. A total dominating set is called minimal if it does not properly contain another total dominating set. In this paper, we study graphs whose all minimal total dominating sets have the same size, referred to as ...
Selim Bahadir +2 more
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Discrete Mathematics, 1984 A dominating [totally dominating] set is a subset D of the vertex set V(G) of a graph G with the property that for each \(x\in V(G)\setminus D\) [for each \(x\in V(G)]\) there exists \(y\in D\) adjacent to x. The domination number \(\gamma\) (G) [the total domination number \(\gamma_ t(G)]\) of G is the minimum number of vertices of a dominating ...
Robert B. Allan +2 more
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Further Results on the Total Roman Domination in Graphs
Mathematics, 2020 Let G be a graph without isolated vertices. A function f : V ( G ) → { 0 , 1 , 2 } is a total Roman dominating function on G if every vertex v ∈ V ( G ) for which f ( v ) = 0 is adjacent to at least one vertex u ...
Abel Cabrera Martínez +2 more
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Bounds on Global Total Domination in Graphs [PDF]
Computer Science Journal of Moldova, 2015 A subset $S$ of vertices in a graph $G$ is a \textit{global total dominating set}, or just GTDS, if $S$ is a \textit{total dominating set} of both $G$ and $\overline{G}$.
Nader Jafari Rad, Elahe Sharifi
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On total domination and total equitable domination in graphs
Malaya Journal of Matematik, 2018 A dominating set $D$ of a graph $G$ is called total if every vertex of $V(G)$ is adjacent to at least one vertex of $D$, equivalently if $N(D)=V(G)$ then $D$ is called total dominating set. A dominating set $D$ is called total equitable dominating set if it is total and for every vertex in $V(G)-D$ there exists a vertex in $D$ such that they are ...
null S. K. Vaidya, null A. D. Parmar
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Disjunctive total domination in graphs [PDF]
Journal of Combinatorial Optimization, 2014 Let $G$ be a graph with no isolated vertex. In this paper, we study a parameter that is a relaxation of arguably the most important domination parameter, namely the total domination number, $γ_t(G)$. A set $S$ of vertices in $G$ is a disjunctive total dominating set of $G$ if every vertex is adjacent to a vertex of $S$ or has at least two vertices in ...
Michael A. Henning, Viroshan Naicker
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