Domination parameters in Mycielski graphs
Bull. Korean Math. Soc. 2021 Vol. 58, No. 4, 829-836
https://doi.org/10.4134/BKMS.b200571
Published online May 7, 2021
Printed July 31, 2021
Young Soo Kwon, Jaeun Lee, Moo Young Sohn
Yeungnam University; Yeungnam University; Changwon National University
Abstract : In this paper, we consider several domination parameters like perfect domination number, locating-domination number, open-locating-domination number, etc.~in the Mycielski graph $M(G)$ of a graph $G$. We found upper bounds for locating-domination number of $M(G)$ and computational formulae for perfect locating-domination number and open locating-domination number of $M(G)$. We also showed that the perfect domination number of $M(G)$ is at least that of $G$ plus $1$ and that for each positive integer $n$, there exists a graph $G_n$ such that the perfect domination number of $M(G_n)$ is equal to that of $G_n$ plus $n$.
Keywords : Mycielski graph, domination number
MSC numbers : Primary 05C69
Supported by : The second author was supported by the Yeungnam University research grants in 2020. The first and third authors were supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (2018R1D1A1B05048450) and (2020R1I1A3A04036669), respectively.
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