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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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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 +4 more
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On the out-domination and in-domination numbers of a digraph
Discrete Mathematics, 1999 AbstractAn out-domination set of a digraph D is a set S of vertices of D such that every vertex of D−S is adjacent from some vertex of S. The minimum cardinality of an out-domination set of D is the out-domination number γ+(D). The in-domination number γ−(D) is defined analogously. It is shown that for every digraph D of order n with no isolates, γ−(D)+
Frank Harary +2 more
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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 +2 more
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On domination and independent domination numbers of a graph
Discrete Mathematics, 1978 AbstractFor a graph G, the definitions of domination number, denoted γ(G), and independent domination number, denoted i(G), are given, and the following results are obtained:Theorem. If G does not have an induced subgraph isomorphic to K1,3, then γ(G) = i(G).Corollary 1. For any graph G, γ(L(G))=i(L(G)), where L(G) is the line graph of G. (This extends
Renu C. Laskar, Robert B. Allan
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AKCE International Journal of Graphs and Combinatorics, 2020 Let be a graph and let be a family of subsets of such that A dominating set of is called an -dominating set if for all The minimum cardinality of an -dominating of is called the -domination number of and is denoted by In this paper we present several ...
Manju Raju +3 more
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Bipartite graphs with close domination and k-domination numbers [PDF]
Open Mathematics, 2020 Abstract Let k k be a positive integer and let G
Ekinci, Gulnaz Boruzanli, Bujtas, Csilla
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Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2015 Let G = (V;E) be a graph. A set S ⊂ V (G) is a hop dominating set of G if for every v ∈ V - S, there exists u ∈ S such that d(u; v) = 2. The minimum cardinality of a hop dominating set of G is called a hop domination number of G and is denoted by γh(G ...
Natarajan C., Ayyaswamy S.K.
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On resolving domination number of special family of graphs
Journal of Physics: Conference Series, 2020 Let G be a simple, finite, and connected graph. A dominating set D is a set of vertices such that each vertex of G is either in D or has at least one neighbor in D.
Y. Wangguway +4 more
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On the Total Outer k-Independent Domination Number of Graphs
Mathematics, 2020 A set of vertices of a graph G is a total dominating set if every vertex of G is adjacent to at least one vertex in such a set. We say that a total dominating set D is a total outer k-independent dominating set of G if the maximum degree of the subgraph ...
A. Cabrera-Martínez +3 more
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