TY  - JOUR
ID  - Dettlaff2019
LB  - Dettlaff2019
AU  - Dettlaff, Magda
AU  - Lemańska, Magdalena
AU  - Miotk, Mateusz
AU  - Topp, Jerzy
AU  - Ziemann, Radosław
AU  - Żyliński, Paweł
TI  - Graphs with equal domination and certified domination numbers
ST  - Graphs with equal domination and certified domination numbers
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2019
VL  - 39
IS  - 6
SP  - 815
EP  - 827
DO  - https://doi.org/10.7494/OpMath.2019.39.6.815
UR  - https://doi.org/10.7494/OpMath.2019.39.6.815
AB  - 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.
KW  - domination
KW  - certified domination
SN  - 1232-9274
ER  -