Bondage number

In the mathematical field of graph theory, the bondage number of a nonempty graph is the cardinality of the smallest set $E$ of edges such that the domination number of the graph with the edges $E$ removed is strictly greater than the domination number of the original graph.^[1]^[2] The concept was introduced by Fink et al.^[3]

References

^ Fink, John Frederick (1990). "The bondage number of a graph". Discrete Mathematics. 86 (1–3): 47–57. doi:10.1016/0012-365X(90)90348-L.
^ Hartnell, Bert L. (1994). "Bounds on the bondage number of a graph". Discrete Mathematics. 128 (1–3): 173–177. doi:10.1016/0012-365X(94)90111-2.
^ Xu, J. M. (2013). "On Bondage Numbers of Graphs: A Survey with Some Comments". International Journal of Combinatorics. 2013 (1): 1–34. arXiv:1204.4010. doi:10.1155/2013/595210.

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[1] Fink, John Frederick (1990). "The bondage number of a graph". Discrete Mathematics. 86 (1–3): 47–57. doi:10.1016/0012-365X(90)90348-L.

[2] Hartnell, Bert L. (1994). "Bounds on the bondage number of a graph". Discrete Mathematics. 128 (1–3): 173–177. doi:10.1016/0012-365X(94)90111-2.

[3] Xu, J. M. (2013). "On Bondage Numbers of Graphs: A Survey with Some Comments". International Journal of Combinatorics. 2013 (1): 1–34. arXiv:1204.4010. doi:10.1155/2013/595210.

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