Results 71 to 80 of about 13,369 (211)
Efficient total domination in digraphs
Journal of Discrete Algorithms, 2012 AbstractWe generalize the concept of efficient total domination from graphs to digraphs. An efficiently total dominating set X of a digraph D is a vertex subset such that every vertex of D has exactly one predecessor in X. We study graphs that permit an orientation having such a set and give complexity results and characterizations.
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On the total Roman domination in trees
Discussiones Mathematicae Graph Theory, 2019 A total Roman dominating function on a graph G is a function f : V (G) → {0, 1, 2} satisfying the following conditions: (i) every vertex u for which f(u) = 0 is adjacent to at least one vertex v for which f(v) = 2 and (ii) the subgraph of G induced by the set of all vertices of positive weight has no isolated vertex.
Marzieh Soroudi +2 more
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Total Roman {3}-Domination: The Complexity and Linear-Time Algorithm for Trees [PDF]
, 2021 Xinyue Liu +3 more
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Augmenting graphs to partition their vertices into a total dominating set and an independent dominating set [PDF]
Opuscula MathematicaA graph \(G\) whose vertex set can be partitioned into a total dominating set and an independent dominating set is called a TI-graph. There exist infinite families of graphs that are not TI-graphs. We define the TI-augmentation number \(\operatorname{ti}(
Teresa W. Haynes, Michael A. Henning
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Signed total domination in graphs
Discrete Mathematics, 2004 The paper continues the study of the signed total domination in graphs which was started by the reviewer. Let \(G\) be a graph with vertex set \(V\). For each \(v\in V\) let \(N(v)\) be the open neighbourhood of \(v\) in \(G\), i.e. the set of all vertices adjacent to \(v\) in \(G\). If \(f\) is a mapping of \(V\) into a number set and \(S\subseteq V\),
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Total domination in inflated graphs
Discrete Applied Mathematics, 2012 AbstractThe inflation GI of a graph G is obtained from G by replacing every vertex x of degree d(x) by a clique X=Kd(x) and each edge xy by an edge between two vertices of the corresponding cliques X and Y of GI in such a way that the edges of GI which come from the edges of G form a matching of GI.
Adel P. Kazemi, Michael A. Henning
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Restricted total domination in graphs
Discrete Mathematics, 2004 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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A note on total co-independent domination in trees [PDF]
, 2022 Abel Cabrera Martínez +3 more
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Total $k$-rainbow domination subdivision number in graphs [PDF]
Computer Science Journal of Moldova, 2020 A total $k$-rainbow dominating function (T$k$RDF) of $G$ is a function $f$ from the vertex set $V(G)$ to the set of all subsets of the set $\{1,\ldots,k\}$ such that (i) for any vertex $v\in V(G)$ with $f(v)=\emptyset$ the condition $\bigcup_{u \in N(v ...
Rana Khoeilar +3 more
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Graphs with large disjunctive total domination number [PDF]
, 2015 Michael A. Henning, Viroshan Naicker
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