Results 11 to 20 of about 17,112 (263)

Characterization of outerplanar graphs with equal 2-domination and domination numbers

Theory and Applications of Graphs, 2022
A {\em $k$-domination number} of a graph $G$ is minimum cardinality of a $k$-dominating set of $G$, where a subset $S \subseteq V(G)$ is a {\em $k$-dominating set} if each vertex $v\in V(G)\setminus S$ is adjacent to at least $k$ vertices in $S$.
Naoki Matsumoto
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On the Paired-Domination Subdivision Number of Trees

Mathematics, 2021
A paired-dominating set of a graph G without isolated vertices is a dominating set of vertices whose induced subgraph has perfect matching. The minimum cardinality of a paired-dominating set of G is called the paired-domination number γpr(G) of G.
Shouliu Wei, Guoliang Hao, Seyed Mahmoud Sheikholeslami, Rana Khoeilar, Hossein Karami   +4 more
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On the edge geodetic and edge geodetic domination numbers of a graph [PDF]

Communications in Combinatorics and Optimization, 2020
In this paper, we study both concepts of geodetic dominating and edge geodetic dominating sets and derive some tight upper bounds on the edge geodetic and the edge geodetic domination numbers.
Vladimir Samodivkin
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On the out-domination and in-domination numbers of a digraph

Discrete Mathematics, 1999
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Gary Chartrand, Frank Harary, Bill Quan Yue   +2 more
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The paired-domination and the upper paired-domination numbers of graphs [PDF]

Opuscula Mathematica, 2015
In this paper we continue the study of paired-domination in graphs. A paired-dominating set, abbreviated PDS, of a graph \(G\) with no isolated vertex is a dominating set of vertices whose induced subgraph has a perfect matching.
Włodzimierz Ulatowski
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Domination and Power Domination in Certain Families of Nanostars Dendrimers

IEEE Access, 2020
Dendrimers are hyper-branched macromolecules having various applications in diverse fields like supra-molecular chemistry, drug delivery and nanotechnology etc.
Tanveer Iqbal, Muhammad Imran, Syed Ahtsham Ul Haq Bokhary   +2 more
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On the Paired-Domination Subdivision Number of a Graph

Mathematics, 2021
In order to increase the paired-domination number of a graph G, the minimum number of edges that must be subdivided (where each edge in G can be subdivided no more than once) is called the paired-domination subdivision number sdγpr(G) of G.
Guoliang Hao, Seyed Mahmoud Sheikholeslami, Mustapha Chellali, Rana Khoeilar, Hossein Karami   +4 more
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The Domination Number of Grids [PDF]

SIAM Journal on Discrete Mathematics, 2011
12 pages, 4 ...
Gonçalves, Daniel, Pinlou, Alexandre, Rao, Michaël, Thomassé, Stéphan   +3 more
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On the domination search number

Discrete Applied Mathematics, 2000
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Fedor V. Fomin, Dieter Kratsch, Haiko Müller   +2 more
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Domination Subdivision Numbers

Discussiones Mathematicae Graph Theory, 2001
A set \(S\) of vertices of a graph \(G\) is a dominating set if every vertex of \(V(G)-S\) is adjacent to some vertex in \(S\). The domination number \(\gamma(G)\) is the minimum cardinality of a dominating set of \(G\), and the domination subdivision number \(\text{sd}_{\gamma}(G)\) is the minimum number of edges that must be subdivided (each edge in \
Teresa W. Haynes, Sandra Mitchell Hedetniemi, Stephen T. Hedetniemi, David Pokrass Jacobs, James A. Knisely, Lucas C. van der Merwe   +5 more
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