Results 11 to 20 of about 398,878 (275)
A Linear Kernel for Planar Total Dominating Set [PDF]
Discrete Mathematics & Theoretical Computer Science, 2018 A total dominating set of a graph $G=(V,E)$ is a subset $D \subseteq V$ such that every vertex in $V$ is adjacent to some vertex in $D$. Finding a total dominating set of minimum size is NP-hard on planar graphs and W[2]-complete on general graphs when ...
Valentin Garnero, Ignasi Sau
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A Novel Hybrid Algorithm for Minimum Total Dominating Set Problem
Mathematics, 2019 The minimum total dominating set (MTDS) problem is a variant of the classical dominating set problem. In this paper, we propose a hybrid evolutionary algorithm, which combines local search and genetic algorithm to solve MTDS.
Fuyu Yuan +4 more
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Graphs whose vertex set can be partitioned 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. We give constructions that yield infinite families of graphs that are TI-graphs, as well as constructions that yield ...
Teresa W. Haynes, Michael A. Henning
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Locating-total dominating sets in twin-free graphs: a conjecture [PDF]
The Electronic Journal of Combinatorics, 2016 A total dominating set of a graph $G$ is a set $D$ of vertices of $G$ such that every vertex of $G$ has a neighbor in $D$. A locating-total dominating set of $G$ is a total dominating set $D$ of $G$ with the additional property that every two distinct ...
Foucaud, Florent, Henning, Michael A.
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Graphs with large disjunctive total domination number [PDF]
Discrete Mathematics & Theoretical Computer Science, 2015 Graph ...
Michael A. Henning, Viroshan Naicker
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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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Maximum Number of Minimum Dominating and Minimum Total Dominating Sets
, 2013 Given a connected graph with domination (or total domination) number \gamma>=2, we ask for the maximum number m_\gamma and m_{\gamma,T} of dominating and total dominating sets of size \gamma.
Godbole, Anant +2 more
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Discrete Applied Mathematics, 2022 The problems of determining locating-dominating, open locating-dominating or locating total-dominating sets of minimum cardinality in a graph G are variations of the classical minimum dominating set problem in G and are all known to be hard for general graphs.
Gabriela Argiroffo +3 more
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Optimal Locating-Total Dominating Sets in Strips of Height 3
Discussiones Mathematicae Graph Theory, 2015 A set C of vertices in a graph G = (V,E) is total dominating in G if all vertices of V are adjacent to a vertex of C. Furthermore, if a total dominating set C in G has the additional property that for any distinct vertices u, v ∈ V \ C the subsets formed
Junnila Ville
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Blocking total dominating sets via edge contractions [PDF]
Theoretical Computer Science, 2021 In this paper, we study the problem of deciding whether the total domination number of a given graph $G$ can be reduced using exactly one edge contraction (called 1-Edge Contraction($ _t$)). We focus on several graph classes and determine the computational complexity of this problem.
Galby, Esther +2 more
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