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Computing locating-total domination number in some rotationally symmetric graphs [PDF]
Science Progress, 2021 Let G = ( V , E ) be a connected graph. A locating-total dominating set in a graph G is a total dominating set S of a G , for every pair of vertices i , j ∈ V ( G ) ∖ S , such that N ( i ) ∩ S ≠ N ( j ) ∩ S .
Hassan Raza +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 ...
Foucaud, Florent, Henning, Michael A.
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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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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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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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Bounds on the Locating-Total Domination Number in Trees
Discussiones Mathematicae Graph Theory, 2020 Given a graph G = (V, E) with no isolated vertex, a subset S of V is called a total dominating set of G if every vertex in V has a neighbor in S. A total dominating set S is called a locating-total dominating set if for each pair of distinct vertices u ...
Wang Kun, Ning Wenjie, Lu Mei
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Coloring, location and domination of corona graphs [PDF]
, 2012 A vertex coloring of a graph $G$ is an assignment of colors to the vertices of $G$ such that every two adjacent vertices of $G$ have different colors. A coloring related property of a graphs is also an assignment of colors or labels to the vertices of a ...
Aguilar, A. Rondón +2 more
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A Note on the Locating-Total Domination in Graphs
Discussiones Mathematicae Graph Theory, 2017 In this paper we obtain a sharp (improved) lower bound on the locating-total domination number of a graph, and show that the decision problem for the locating-total domination is NP-complete.
Miller Mirka +4 more
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Locating total dominating sets in the join, corona and composition of graphs
Applied Mathematical Sciences, 2014 Let G =( V (G),E(G)) be a connected graph. A subset S of V (G) is a total dominating set of G if every vertex of G is adjacent to some vertex in S. The set NG(v) is the set of all vertices of G adjacent to v .A subset S of V (G) is a locating set of G if NG(u)∩SNG(v)∩S for every two distinct vertices u and v in V (G) \ S.
Benjamin N. Omamalin +2 more
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