Results 11 to 20 of about 11,901,808 (241)
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
doaj +5 more sources
Optimal Locating-Total Dominating Sets in Strips of Height 3 [PDF]
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
doaj +7 more sources
Partitioning a graph into a dominating set, a total dominating set, and something else [PDF]
Discussiones Mathematicae Graph Theory, 2010 A recent result of Henning and Southey (A note on graphs with disjoint dominating and total dominating set, {\it Ars Comb.} {\bf 89} (2008), 159--162) implies that every connected graph of minimum degree at least three has a dominating set $D$ and a total dominating set $T$ which are disjoint.
Michael A. Henning +2 more
openaire +5 more sources
A Note on Non-Dominating Set Partitions in Graphs [PDF]
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
doaj +3 more sources
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
doaj +2 more sources
Trees with unique minimum total dominating sets [PDF]
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
openaire +2 more sources
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
doaj +3 more sources
Minimal graphs with disjoint dominating and total dominating sets [PDF]
Discussiones Mathematicae Graph Theory23 pages, 12 ...
Michael A. Henning, Jerzy Topp
openaire +5 more sources
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
doaj +2 more sources
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
openaire +4 more sources