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Disjoint dominating and total dominating sets in graphs
Discrete Applied Mathematics, 2010 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Michael A. Henning +3 more
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Locating and total dominating sets in trees
Discrete Applied Mathematics, 2006 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Teresa W. Haynes +2 more
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A Note on Non-Dominating Set Partitions in Graphs
Discussiones Mathematicae Graph Theory, 2016 A set S of vertices of a graph G is a dominating set if every vertex not in S is adjacent to a vertex of S and is a total dominating set if every vertex of G is adjacent to a vertex of S.
Desormeaux Wyatt J. +2 more
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Study on a Strong and Weak n-Connected Total Perfect k-Dominating set in Fuzzy Graphs [PDF]
Mathematics, 2022 In this paper, the concept of a strong n-Connected Total Perfect k-connected total perfect k-dominating set and a weak n-connected total perfect k-dominating set in fuzzy graphs is introduced.
Krishnasamy Elavarasan +3 more
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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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Trees with unique minimum total dominating sets
Discussiones Mathematicae Graph Theory, 2002 A set \(S\) of vertices of a graph \(G\) is a total dominating set if every vertex of \(G\) is adjacent to some vertex in \(S\). Three equivalent conditions for a tree to have a unique minimum total dominating set together with a constructive characterization of such trees are given.
Teresa W. Haynes, Michael A. Henning
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Minimal graphs with disjoint dominating and total dominating sets
Discussiones Mathematicae Graph Theory23 pages, 12 ...
Michael A. Henning, Jerzy Topp
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An Approximation Algorithm for a Variant of Dominating Set Problem
Axioms, 2023 In this paper, we consider a variant of dominating set problem, i.e., the total dominating set problem. Given an undirected graph G=(V,E), a subset of vertices T⊆V is called a total dominating set if every vertex in V is adjacent to at least one vertex ...
Limin Wang, Wenqi Wang
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Polyhedra Associated with Open Locating-Dominating and Locating Total-Dominating Sets in Graphs [PDF]
, 2020 The problems of determining 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. A typical line of attack is therefore to determine the cardinality of minimum such sets in special graphs.
Argiroffo, Gabriela +3 more
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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 vertices outside $D$ have distinct neighbors in $D$; that is, for distinct vertices $u$ and $v ...
Florent Foucaud, Michael A. Henning
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