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Domination subdivision numbers in graphs
2004A set \(S\) of vertices of a graph \(G\) is a dominating set if each vertex outside \(S\) has a neighbor in \(S\). The domination number \(\gamma(G)\) of \(G\) is the minimum cardinality of a dominating set of \(G\). An edge \(uv\) in \(G\) is subdivided if the edge \(uv\) is deleted, but a new vertex \(x\) is added, along with two new edges \(xu\) and
Favaron, Odile +2 more
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On the rainbow domination subdivision numbers in graphs
Asian-European Journal of Mathematics, 2016A [Formula: see text]-rainbow dominating function (2RDF) of a graph [Formula: see text] is a function [Formula: see text] from the vertex set [Formula: see text] to the set of all subsets of the set [Formula: see text] such that for any vertex [Formula: see text] with [Formula: see text] the condition [Formula: see text] is fulfilled, where [Formula ...
Dehgardi, N. +3 more
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Influence of edge subdivision on the convex domination number.
Australas. J Comb., 2012We study the influence of edge subdivision on the convex domination number. We show that in general an edge subdivision can arbitrarily increase and arbitrarily decrease the convex domination number. We also find some bounds for unicyclic graphs and we investigate graphs G for which the convex domination number changes after subdivision of any edge in ...
Magda Dettlaff, Magdalena Lemańska
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Domination Uniform Subdivision Number of Graph
International Journal of Mathematics Trends and Technology, 2015Let G = (V, E) be a simple undirected graph. A subset D of V (G) is said to be dominating set if every vertex of V (G) − D is adjacent to at least one vertex in D. The minimum cardinality taken over all minimal dominating sets of G is the domination number of G and is denoted by γ(G). The domination uniform subdivision number of G is the least positive
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Semitotal domination subdivision numbers of graphs
Journal of Discrete Mathematical Sciences and Cryptography, 2020Qin Chen, Yunfang Tang
exaly
An Upper Bound for the Total Domination Subdivision Number of a Graph
Graphs and Combinatorics, 2010Rana Khoeilar +2 more
exaly
On the domination subdivision numbers of trees.
Australas. J Comb., 2010B. Sharada, Nandappa D. Soner
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Results on Total Restrained Domination number and subdivision number for certain graphs
Journal of Discrete Mathematical Sciences and Cryptography, 2015Bijan Davvaz, P Jeyanthi
exaly
Total domination and total domination subdivision numbers.
Australas. J Comb., 2007Odile Favaron +2 more
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Np-completeness and bounds for disjunctive total domination subdivision
Journal of Combinatorial OptimizationCanan Ciftci, Aysun Aytaç
exaly