Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

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Bull. Korean Math. Soc. 2021; 58(4): 829-836

Online first article May 7, 2021      Printed July 31, 2021

https://doi.org/10.4134/BKMS.b200571

Copyright © The Korean Mathematical Society.

Domination parameters in Mycielski graphs

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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