Results 21 to 30 of about 11,901,808 (241)
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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Some results on the open locating-total domination number in graphs [PDF]
Journal of Mahani Mathematical Research, 2023 In this paper, we generalize the concept of an open locating-dominating set in graphs. We introduce a concept as an open locating-total dominating set in graphs that is equivalent to the open neighborhood locating-dominating set.
Fateme Movahedi, Mohammad Hadi Akhbari
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More on the Enumeration of Some Kind of Dominating Sets in Cactus Chains [PDF]
Mathematics Interdisciplinary Research, 2022 A non-empty set S ⊆ V is a dominating set, if every vertex not in S is adjacent to at least one vertex in S, and S is a total dominating set, if every vertex of V is adjacent to some vertices of S.
Somayeh Jahari, Saeid Alikhani
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A linear-time algorithm to compute total $[1,2]$-domination number of block graphs [PDF]
AUT Journal of Mathematics and Computing, 2020 Let $G=(V, E)$ be a simple graph without isolated vertices. A set $D\subseteq V$ is a total $[1,2]$-dominating set if for every vertex $v\in V , 1\leq |N(v)\cap D|\leq 2$.
Pouyeh Sharifani +2 more
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Nordhaus-Gaddum bounds for upper total domination [PDF]
Opuscula Mathematica, 2022 A set \(S\) of vertices in an isolate-free graph \(G\) is a total dominating set if every vertex in \(G\) is adjacent to a vertex in \(S\). A total dominating set of \(G\) is minimal if it contains no total dominating set of \(G\) as a proper subset. The
Teresa W. Haynes, Michael A. Henning
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Disjoint total dominating sets in near‐triangulations
Journal of Graph Theory, 2023 AbstractWe show that every simple planar near‐triangulation with minimum degree at least three contains two disjoint total dominating sets. The class includes all simple planar triangulations other than the triangle. This affirms a conjecture of Goddard and Henning.
P. Francis +3 more
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Approximation hardness of dominating set problems in bounded degree graphs [PDF]
, 2008 We study approximation hardness of the Minimum Dominating Set problem and its variants in undirected and directed graphs. Using a similar result obtained by Trevisan for Minimum Set Cover we prove the first explicit approximation lower bounds for various
Chlebikova, Janka +3 more
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dib-lab/2022-dominating-set-differential-abundance-example: preprint version 1.0
, 2022 A reproducible example demonstrating an example workflow for performing dominating set differential abundance ...
Taylor Reiter
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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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Blocking total dominating sets via edge contractions
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($γ_t$)). We focus on several graph classes and determine the computational complexity of this problem.
Esther Galby, Felix Mann, Bernard Ries
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