Bondage Number of 1-Planar Graph
Qiaoling Ma, Sumei Zhang, Jihui Wang
DOI: 10.4236/am.2010.12013   PDF   HTML     4,565 Downloads   8,835 Views   Citations


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.

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Q. Ma, S. Zhang and J. Wang, "Bondage Number of 1-Planar Graph," Applied Mathematics, Vol. 1 No. 2, 2010, pp. 101-103. doi: 10.4236/am.2010.12013.

Conflicts of Interest

The authors declare no conflicts of interest.


[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.

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