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Upper bounds on the paired-domination number
Applied Mathematics Letters, 2008 A set S of vertices in a graph G is a paired-dominating set of G if every vertex of G is adjacent to some vertex in S and the subgraph induced by S contains a perfect matching.
Xue-Gang Chen +2 more
exaly +4 more sources
Graphs and Combinatorics, 2022 A set S of vertices in a graph G is a paired dominating set if every vertex of G is adjacent to a vertex in S and the subgraph induced by S contains a perfect matching (not necessarily as an induced subgraph).
Aleksandra Gorzkowska +3 more
semanticscholar +3 more sources
Total domination versus paired domination [PDF]
Discussiones Mathematicae Graph Theory, 2011 A dominating set of a graph G is a vertex subset that any vertex of G either belongs to or is adjacent to. A total dominating set is a dominating set whose induced subgraph does not contain isolated vertices.
Schaudt, Oliver
core +5 more sources
Journal of New Theory, 2023 In this study, transformation graphs obtained from the concept of the total graph and the result of its paired domination number for some special graph families are discussed.
Hande Tunçel Gölpek
doaj +2 more sources
Minimal Graphs with Disjoint Dominating and Paired-Dominating Sets
Discussiones Mathematicae Graph Theory, 2021 A subset D ⊆ VG is a dominating set of G if every vertex in VG – D has a neighbor in D, while D is a paired-dominating set of G if D is a dominating set and the subgraph induced by D contains a perfect matching.
Henning Michael A., Topp Jerzy
doaj +4 more sources
Paired domination stability in graphs
Ars Mathematica Contemporanea, 2021 A set S of vertices in a graph G is a paired dominating set if every vertex of G is adjacent to a vertex in S and the subgraph induced by S contains a perfect matching (not necessarily as an induced subgraph).
Aleksandra Gorzkowska +3 more
semanticscholar +4 more sources
Networks, 1998 In a graph G = (V, E) if we think of each vertex s as the possible location for a guard capable of protecting each vertex in its closed neighborhood N[s], then domination requires every vertex to be protected.
Haynes, Teresa W., Slater, Peter J.
core +3 more sources
Equitable and Paired Equitable Domination in Inflated Graphs and Their Complements [PDF]
Axioms, 2023 Domination plays an indispensable role in graph theory. Various types of domination explore various types of applications. Equal-status people work together and interlace with each other easily.
Narayanan Kumaran +4 more
doaj +2 more sources
Block Graphs with Large Paired Domination Multisubdivision Number
Discussiones Mathematicae Graph Theory, 2021 The paired domination multisubdivision number of a nonempty graph G, denoted by msdpr(G), is the smallest positive integer k such that there exists an edge which must be subdivided k times to increase the paired domination number of G.
Mynhardt Christina M., Raczek Joanna
doaj +2 more sources
Complexity of Paired Domination in AT-free and Planar Graphs [PDF]
SSRN Electronic Journal, 2021 For a graph $G=(V,E)$, a subset $D$ of vertex set $V$, is a dominating set of $G$ if every vertex not in $D$ is adjacent to atleast one vertex of $D$. A dominating set $D$ of a graph $G$ with no isolated vertices is called a paired dominating set (PD-set)
Vikash Tripathi +4 more
semanticscholar +4 more sources