Browse > Article
http://dx.doi.org/10.4134/BKMS.b200571

DOMINATION PARAMETERS IN MYCIELSKI GRAPHS  

Kwon, Young Soo (Department of Mathematics Yeungnam University)
Lee, Jaeun (Department of Mathematics Yeungnam University)
Sohn, Moo Young (Department of Mathematics Changwon National University)
Publication Information
Bulletin of the Korean Mathematical Society / v.58, no.4, 2021 , pp. 829-836 More about this Journal
Abstract
In this paper, we consider several domination parameters like perfect domination number, locating-domination number, open-locatingdomination 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 Gn such that the perfect domination number of M(Gn) is equal to that of Gn plus n.
Keywords
Mycielski graph; domination number;
Citations & Related Records
연도 인용수 순위
  • Reference
1 G. J. Chang, L. Huang, and X. Zhu, Circular chromatic numbers of Mycielski's graphs, Discrete Math. 205 (1999), no. 1-3, 23-37. https://doi.org/10.1016/S0012-365X(99)00033-3   DOI
2 G. Fan, Circular chromatic number and Mycielski graphs, Combinatorica 24 (2004), no. 1, 127-135. https://doi.org/10.1007/s00493-004-0008-9   DOI
3 T. W. Haynes, S. T. Hedetniemi, and P. J. Slater, Fundamentals of domination in graphs, Monographs and Textbooks in Pure and Applied Mathematics, 208, Marcel Dekker, Inc., New York, 1998.
4 W. Lin, J. Wu, P. C. B. Lam, and G. Gu, Several parameters of generalized Mycielskians, Discrete Appl. Math. 154 (2006), no. 8, 1173-1182. https://doi.org/10.1016/j.dam.2005.11.001   DOI
5 M. Larsen, J. Propp, and D. Ullman, The fractional chromatic number of Mycielski's graphs, J. Graph Theory 19 (1995), no. 3, 411-416. https://doi.org/10.1002/jgt.3190190313   DOI
6 J. Mycielski, Sur le coloriage des graphs, Colloq. Math. 3 (1955), 161-162. https://doi.org/10.4064/cm-3-2-161-162   DOI
7 X. Chen and H. Xing, Domination parameters in Mycielski graphs, Util. Math. 71 (2006), 235-244.
8 D. D.-F. Liu, Circular chromatic number for iterated Mycielski graphs, Discrete Math. 285 (2004), no. 1-3, 335-340. https://doi.org/10.1016/j.disc.2004.01.020   DOI
9 D. A. Mojdeh and N. J. Rad, On domination and its forcing in Mycielski's graphs, Sci. Iran. 15 (2008), no. 2, 218-222.
10 C. Tardif, Fractional chromatic numbers of cones over graphs, J. Graph Theory 38 (2001), no. 2, 87-94. https://doi.org/10.1002/jgt.1025   DOI