Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
권호 표지
DOI QR코드

DOI QR Code

THE BONDAGE NUMBER OF C3×Cn

  • Sohn, Moo-Young (DEPARTMENT OF APPLIED MATHEMATICS CHANGWON NATIONAL UNIVERSITY) ;
  • Xudong, Yuan (DEPARTMENT OF MATHEMATICS GUANGXI NORMAL UNIVERSITY) ;
  • Jeong, Hyeon-Seok (DEPARTMENT OF APPLIED MATHEMATICS CHANGWON NATIONAL UNIVERSITY)
  • Published : 2007.11.30
Download PDF
⟨ Previous Next ⟩

Abstract

The domination number ${\gamma}(G)$ of a graph G=(V,E) is the minimum cardinality of a subset of V such that every vertex is either in the set or is adjacent to some vertex in the set. The bondage number of b(G) of a graph G is the cardinality of a smallest set of edges whose removal from G results in a graph with domination number greater than ${\gamma}(G)$. In this paper, we calculate the bondage number of the Cartesian product of cycles $C_3\;and\;C_n$ for all n.

Keywords

References

  1. T. Chang and E. Clark, The domination numbers of the $5{\times}n\;and\;6{\times}n$ grid graphs, J. Graph Theory 17 (1993), no. 1, 81-107 https://doi.org/10.1002/jgt.3190170110
  2. J. E. Dunbar, T. W. Haynes, U. Teschner, and L. Volkmann, `Bondage, Insensitivity, and Reinforcement' in Domination in graphs advanced topics (Marcel Decker, New York,1998), 471-489
  3. M. El-Zahar and C. M. Pareek, Domination number of products of graphs, Ars Combin. 31 (1991), 223-227
  4. J. F. Fink, M. S. Jacobson, L. F. Kinch, and J. Roberts, The bondage number of a graph, Discrete Math. 86 (1990), no. 1-3, 47-57 https://doi.org/10.1016/0012-365X(90)90348-L
  5. B. L. Hartnell and D. F. Rall, Bounds on the bondage number of a graph, Discrete Math. 128 (1994), no. 1-3, 173-177 https://doi.org/10.1016/0012-365X(94)90111-2
  6. B. L. Hartnell and D. F. Rall, A characterization of trees in which no edge is essential to the domination number, Ars Combin. 33 (1992), 65-76
  7. L. Y. Kang and J. J. Yuan, Bondage number of planar graphs, Discrete Math. 222 (2000), no. 1-3, 191-198 https://doi.org/10.1016/S0012-365X(99)00405-7
  8. L. Y. Kang, M. Y. Sohn, and H. K. Kim, Bondage number of the discrete torus $C{\subseteq}n{\times}C{\subseteq}4$, Discrete Math. 303 (2005), no. 1-3, 80-86 https://doi.org/10.1016/j.disc.2004.12.019
  9. S. Klav.zar and S. Sandi, Norbert Dominating Cartesian products of cycles, Discrete Appl. Math. 59 (1995), no. 2, 129-136 https://doi.org/10.1016/0166-218X(93)E0167-W

Cited by

  1. The total bondage number of grid graphs vol.160, pp.16-17, 2012, https://doi.org/10.1016/j.dam.2012.06.012
  2. On Bondage Numbers of Graphs: A Survey with Some Comments vol.2013, 2013, https://doi.org/10.1155/2013/595210
  3. Bondage number of the strong product of two trees vol.230, 2017, https://doi.org/10.1016/j.dam.2017.06.019
  4. The bondage number of the strong product of a complete graph with a path and a special starlike tree vol.08, pp.01, 2016, https://doi.org/10.1142/S1793830916500063
  5. Bondage Numbers ofC4Bundles over a CycleCn vol.2013, 2013, https://doi.org/10.1155/2013/520251
  6. Upper bounds on the bondage number of the strong product of a graph and a tree 2017, https://doi.org/10.1080/00207160.2017.1291931
  7. Bondage number of mesh networks vol.7, pp.5, 2012, https://doi.org/10.1007/s11464-012-0173-x
  8. Bondage number of strong product of two paths vol.10, pp.2, 2015, https://doi.org/10.1007/s11464-014-0391-5