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Further results on the total Italian domination number of trees
AIMS Mathematics, 2023 Let $ f:V(G)\rightarrow \{0, 1, 2\} $ be a function defined from a connected graph $ G $. Let $ W_i = \{x\in V(G): f(x) = i\} $ for every $ i\in \{0, 1, 2\} $. The function $ f $ is called a total Italian dominating function on $ G $ if $ \sum_{v\in N(x)}
Abel Cabrera-Martínez +2 more
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Hop total Roman domination in graphs
AKCE International Journal of Graphs and Combinatorics, 2023 In this article, we initiate a study of hop total Roman domination defined as follows: a hop total Roman dominating function (HTRDF) on a graph [Formula: see text] is a function [Formula: see text] such that for every vertex u with f(u) = 0 there exists ...
H. Abdollahzadeh Ahangar +3 more
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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 Italian domatic number of graphs [PDF]
Computer Science Journal of Moldova, 2023 Let $G$ be a graph with vertex set $V(G)$. An \textit{Italian dominating function} (IDF) on a graph $G$ is a function $f:V(G)\longrightarrow \{0,1,2\}$ such that every vertex $v$ with $f(v)=0$ is adjacent to a vertex $u$ with $f(u)=2$ or to two ...
Seyed Mahmoud Sheikholeslami +1 more
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Neighbourhood total domination in graphs [PDF]
Opuscula Mathematica, 2011 Let \(G = (V,E)\) be a graph without isolated vertices. A dominating set \(S\) of \(G\) is called a neighbourhood total dominating set (ntd-set) if the induced subgraph \(\langle N(S)\rangle\) has no isolated vertices.
S. Arumugam, C. Sivagnanam
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Total Roman domination subdivision number in graphs [PDF]
Communications in Combinatorics and Optimization, 2020 A {\em Roman dominating function} on a graph $G$ is a function $f:V(G)\rightarrow \{0,1,2\}$ satisfying the condition that every vertex $u$ for which $f(u)=0$ is adjacent to at least one vertex $v$ for which $f(v)=2$.
Jafar Amjad
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Independent Transversal Total Domination Versus Total Domination in Trees
Discussiones Mathematicae Graph Theory, 2021 A subset of vertices in a graph G is a total dominating set if every vertex in G is adjacent to at least one vertex in this subset. The total domination number of G is the minimum cardinality of any total dominating set in G and is denoted by γt(G).
Martínez Abel Cabrera +2 more
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Fair Total Domination Number in Cactus Graphs
Discussiones Mathematicae Graph Theory, 2021 For k ≥ 1, a k-fair total dominating set (or just kFTD-set) in a graph G is a total dominating set S such that |N(v) ∩ S| = k for every vertex v ∈ V\S. The k-fair total domination number of G, denoted by ftdk(G), is the minimum cardinality of a kFTD-set.
Hajian Majid, Rad Nader Jafari
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Trees with equal total domination and game total domination numbers
Discrete Applied Mathematics, 2017 23 pages, 5 figures, 22 ...
Michael A. Henning, Douglas F. Rall
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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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