Browsing by Author "Dettlaff, Magda"

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Access status: Open Access ,
Edge subdivision and edge multisubdivision versus some domination related parameters in generalized corona graphs
(2016) Dettlaff, Magda; Raczek, Joanna Patrycja; Yero, Ismael González
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 $xv$. The domination subdivision number of a graph $G$ is the minimum number of edges of $G$ which must be subdivided (where each edge can be subdivided at most once) in order to increase the domination number. Also, the domination multisubdivision number of $G$ is the minimum number of subdivisions which must be done in one edge such that the domination number increases. Moreover, the concepts of paired domination and independent domination subdivision (respectively multisubdivision) numbers are defined similarly. In this paper we study the domination, paired domination and independent domination (subdivision and multisubdivision) numbers of the generalized corona graphs.
Access status: Open Access ,
Graphs with equal domination and certified domination numbers
(Wydawnictwa AGH, 2019) Dettlaff, Magda; Lemańska, Magdalena; Miotk, Mateusz; Topp, Jerzy; Ziemann, Radosław; Żyliński, Paweł
A set $D$ of vertices of a graph $G=(V_{G},E_{G})$ is a dominating set of $G$ if every vertex in $V_{G}-D$ is adjacent to at least one vertex in $D$. The domination number (upper domination number, respectively) of $G$, denoted by $\gamma(G)$ ($\Gamma(G)$, respectively), is the cardinality of a smallest (largest minimal, respectively) dominating set of $G$. A subset $D\subseteq V_G$ is called a certified dominating set of $G$ if $D$ is a dominating set of $G$ and every vertex in $D$ has either zero or at least two neighbors in $V_{G}-D$. The cardinality of a smallest (largest minimal, respectively) certified dominating set of $G$ is called the certified (upper certified, respectively) domination number of $G$ and is denoted by $\gamma_{\rm cer}(G)$ ($\Gamma_{\rm cer}(G)$, respectively). In this paper relations between domination, upper domination, certified domination and upper certified domination numbers of a graph are studied.