Bondage Number of 1-Planar Graph

Qiaoling Ma, Sumei Zhang, Jihui Wang

.

DOI: 10.4236/am.2010.12013                

Abstract

The bondage number of a nonempty graph G is the cardinality of a smallest set of edges whose removal from G results in a graph a domination number greater than the domination number of G. In this paper, we prove that for a 1-planar graph G.

Keywords

Domination Number, Bondage number, 1-Planar Graph, Combinatorial Problem

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	D. Bauer. F. Harry, J. Nieminen and C. L. Suffel, “Domination Alteration Sets in Graphs,” Discrete Mathematics, Vol. 47, 1983, pp. 153-161.
[2]	U. Teschner, “A New Upper Bound for the Bondage Number of Graphs with Small Domination Number,” Australasian Journal of Combinatorics, Vol. 12, 1995, pp. 27-35.
[3]	L. Kang and J. Yuan, “Bondage Number of Planar Graphs,” Discrete Mathematics, Vol. 222, No. 1-3, 2000, pp. 191-198.
[4]	B. L. Hartnell and D. F. Rall, “Bounds on the Bondage Number of a Graph,” Discrete Mathematics, Vol. 128, No. 1-3, 1994, pp. 173-177.
[5]	B. L. Hartnell and D. F. Rall, “A Bound on the Size of a Graph with Given Order and Bondage Number,” Discrete Mathematics, Vol. 197/198, 1999, pp. 409-413.
[6]	U. Teschner, “New Results about the Bondage Number of a Graph,” Discrete Mathematics, Vol. 171, No. 1-3, 1997, pp. 249-259.
[7]	I. Fabrici, “The Structure of 1-Planar Graphs,” Discrete Mathematics, Vol. 307, No. 1, 2007, pp. 854-865.