Results 1 to 10 of about 5,038,045 (306)
An independent dominating set in the complement of a minimum dominating set of a tree [PDF]
Applied Mathematics Letters, 2009 We prove that for every tree T of order at least 2 and every minimum dominating set D of T which contains at most one endvertex of T, there is an independent dominating set I of T which is disjoint from D.
Löwenstein, Christian +2 more
core +2 more sources
Partitioning a graph into a dominating set, a total dominating set, and something else [PDF]
Discussiones Mathematicae Graph Theory, 2009 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 ...
Löwenstein, Christian +4 more
core +5 more sources
A note on partitioning the vertex set of a graph into a dominating set and a locating dominating set
The Electronic Journal of CombinatoricsA set S of vertices in a graph G is a dominating set of G if every vertex not in S has a neighbor in S , where two vertices are neighbors if they are adjacent.
Chakraborty, Dipayan +3 more
core +4 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
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 +2 more sources
Efficient Domination In Fuzzy Graphs and Intuitionistic Fuzzy Graphs in Strong and weak forms [PDF]
E3S Web of Conferences, 2023 This work defines the concepts of strong efficient dominating set and intuitionistic fuzzy graph. We also introduce an intuitionistic fuzzy graph and a strong efficient dominating number of fuzzy graphs.
S Rajeev Gandhi +4 more
doaj +1 more source
On minimum intersections of certain secondary dominating sets in graphs [PDF]
Opuscula Mathematica, 2023 In this paper we consider secondary dominating sets, also named as \((1,k)\)-dominating sets, introduced by Hedetniemi et al. in 2008. In particular, we study intersections of the \((1,1)\)-dominating sets and proper \((1,2)\)-dominating sets.
Anna Kosiorowska +2 more
doaj +1 more source
Reconfiguration of Dominating Sets [PDF]
Journal of Combinatorial Optimization, 2014 12 pages, 4 ...
Akira Suzuki 0001 +2 more
openaire +5 more sources
Dominating Sets and Connected Dominating Sets in Dynamic Graphs [PDF]
CoRR, 2019 In this paper we study the dynamic versions of two basic graph problems: Minimum Dominating Set and its variant Minimum Connected Dominating Set. For those two problems, we present algorithms that maintain a solution under edge insertions and edge deletions in time $O(Δ\cdot \text{polylog}~n)$ per update, where $Δ$ is the maximum vertex degree in the ...
Hjuler N. +3 more
openaire +7 more sources