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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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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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Inequalities involving independence domination, $f$-domination, connected and total $f$-domination numbers [PDF]
, 1978 summary:Let $f$ be an integer-valued function defined on the vertex set $V(G)$ of a graph $G$. A subset $D$ of $V(G)$ is an $f$-dominating set if each vertex $x$ outside $D$ is adjacent to at least $f(x)$ vertices in $D$.
Allan, Robert B. +7 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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On signed majority total domination in graphs [PDF]
, 2005 summary:We initiate the study of signed majority total domination in graphs. Let $G=(V,E)$ be a simple graph. For any real valued function $f\: V \rightarrow \mathbb{R}$ and ${S\subseteq V}$, let $f(S)=\sum _{v\in S}f(v)$.
Sun, Liang +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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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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Total Dominator Colorings in Cycles [PDF]
, 2012 Determining the total dominator chromatic number in ...
Vijayalekshmi, A., A. Vijayalekshmi
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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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