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On domination multisubdivision number of unicyclic graphs [PDF]
Opuscula Mathematica, 2018 The paper continues the interesting study of the domination subdivision number and the domination multisubdivision number. On the basis of the constructive characterization of the trees with the domination subdivision number equal to 3 given in [H. Aram,
Joanna Raczek
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Total Domination Multisubdivision Number of a Graph [PDF]
Discussiones Mathematicae Graph Theory, 2015 The domination multisubdivision number of a nonempty graph G was defined in [3] as the minimum positive integer k such that there exists an edge which must be subdivided k times to increase the domination number of G.
Avella-Alaminos Diana +3 more
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Block Graphs with Large Paired Domination Multisubdivision Number [PDF]
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
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Domination Subdivision and Domination Multisubdivision Numbers of Graphs [PDF]
Discussiones Mathematicae Graph Theory, 2019 The domination subdivision number sd(G) of a graph G is the minimum number of edges that must be subdivided (where an edge can be subdivided at most once) in order to increase the domination number of G. It has been shown [10] that sd(T) ≤ 3 for any tree
Dettlaff Magda +2 more
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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 +2 more
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Changing of the domination number of a graph: edge multisubdivision and edge removal [PDF]
Mathematica Bohemica, 2017 For a graphical property $\mathcal{P}$ and a graph $G$, a subset $S$ of vertices of $G$ is a $\mathcal{P}$-set if the subgraph induced by $S$ has the property $\mathcal{P}$.
Vladimir Samodivkin
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Some of the next articles are maybe not open access.
Paired domination subdivision and multisubdivision numbers of graphs
Journal of Combinatorial Mathematics and Combinatorial Computing, 2020Summary: The paired domination subdivision number \(sd_{pr}(G)\) of a graph \(G\) is the minimum number of edges that must be subdivided (where an edge can be subdivided at most once) in order to increase the paired domination number of \(G\). We prove that the decision problem of the paired domination subdivision number is NP-complete even for ...
Joanna Raczek, Magda Dettlaff
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Semitotal Domination Multisubdivision Number of a Graph
Iranian Journal of Science, 2023openaire +1 more source