Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
권호 표지
DOI QR코드

DOI QR Code

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)
  • Received : 2020.07.02
  • Accepted : 2020.11.02
  • Published : 2021.07.31
Download PDF
⟨ Previous Next ⟩

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

Acknowledgement

The authors are grateful for the referee's constructive remarks and suggestions.

References

  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
  2. X. Chen and H. Xing, Domination parameters in Mycielski graphs, Util. Math. 71 (2006), 235-244.
  3. G. Fan, Circular chromatic number and Mycielski graphs, Combinatorica 24 (2004), no. 1, 127-135. https://doi.org/10.1007/s00493-004-0008-9
  4. 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.
  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
  6. 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
  7. 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
  8. D. A. Mojdeh and N. J. Rad, On domination and its forcing in Mycielski's graphs, Sci. Iran. 15 (2008), no. 2, 218-222.
  9. J. Mycielski, Sur le coloriage des graphs, Colloq. Math. 3 (1955), 161-162. https://doi.org/10.4064/cm-3-2-161-162
  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