Results 21 to 30 of about 1,996 (260)

γ-paired dominating graphs of cycles [PDF]

Opuscula Mathematica, 2022
A paired dominating set of a graph \(G\) is a dominating set whose induced subgraph contains a perfect matching. The paired domination number, denoted by \(\gamma_{pr}(G)\), is the minimum cardinality of a paired dominating set of \(G\).
Pannawat Eakawinrujee, Nantapath Trakultraipruk   +1 more
doaj   +1 more source

Bounding the paired-domination number of a tree in terms of its annihilation number

Filomat, 2014
A paired-dominating set of a graph G=(V, E) with no isolated vertex is a dominating set of vertices whose induced subgraph has a perfect matching. The paired-domination number of G, denoted by ?pr(G), is the minimum cardinality of a paired-dominating set of G.
Nasrin Dehgardi, Seyed Mahmoud Sheikholeslami, Abdollah Khodkar   +2 more
openalex   +3 more sources

Unique Minimum Semipaired Dominating Sets in Trees

Discussiones Mathematicae Graph Theory, 2023
Let G be a graph with vertex set V. A subset S ⊆ V is a semipaired dominating set of G if every vertex in V \ S is adjacent to a vertex in S and S can be partitioned into two element subsets such that the vertices in each subset are at most distance two ...
Haynes Teresa W., Henning Michael A.
doaj   +1 more source

Results of Paired Domination of Some Special Graph Families on Transformation Graphs: $G^{xy+}$ and $G^{xy-}$

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   +1 more source

γ-Paired dominating graphs of lollipop, umbrella and coconut graphs

Electronic Journal of Graph Theory and Applications, 2023
A paired dominating set of a graph G is a dominating set whose induced subgraph has a perfect matching. The paired domination number γpr(G) of G is the minimum cardinality of a paired dominating set. A paired dominating set D is a γpr(G)-set if |D|=γpr(G)
Pannawat Eakawinrujee, Nantapath Trakultraipruk   +1 more
doaj   +1 more source

Neighbourhood total domination in graphs [PDF]

Opuscula Mathematica, 2011
Let \(G = (V,E)\) be a graph without isolated vertices. A dominating set \(S\) of \(G\) is called a neighbourhood total dominating set (ntd-set) if the induced subgraph \(\langle N(S)\rangle\) has no isolated vertices.
S. Arumugam, C. Sivagnanam
doaj   +1 more source

Edge subdivision and edge multisubdivision versus some domination related parameters in generalized corona graphs [PDF]

Opuscula Mathematica, 2016
Given a graph \(G=(V,E)\), the subdivision of an edge \(e=uv\in E(G)\) means the substitution of the edge \(e\) by a vertex \(x\) and the new edges \(ux\) and \(xv\).
Magda Dettlaff, Joanna Raczek, Ismael G. Yero   +2 more
doaj   +1 more source

A note on the upper bound for the paired-domination number of a graph with minimum degree at least two [PDF]

Networks, 2010
Summary: In this note, we give a counter example to show that the proof of a main result obtained by \textit{T. W. Haynes} and \textit{P. J. Slater} [Networks 32, No.3, 199--206 (1998; Zbl 0997.05074), Theorem 12] is inaccurate. Here, we give a complete proof of the result.
Shenwei Huang, Erfang Shan
openalex   +3 more sources

Total and paired domination numbers of toroidal meshes [PDF]

Journal of Combinatorial Optimization, 2012
Let $G$ be a graph without isolated vertices. The total domination number of $G$ is the minimum number of vertices that can dominate all vertices in $G$, and the paired domination number of $G$ is the minimum number of vertices in a dominating set whose induced subgraph contains a perfect matching.
Fu-Tao Hu, Jun-Ming Xu 0001
openaire   +3 more sources

Paired-Domination Number of Some Graphs

Jayson N Payla
openalex   +2 more sources