Copyright © 2013 Jun-Ming Xu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The domination number of a graph is the smallest number of vertices which dominate all remaining vertices by edges of . The bondage number of a nonempty graph is the smallest number of edges whose removal from results in a graph with domination number greater than the domination number of . The concept of the bondage number was formally introduced by Fink et al. in 1990. Since then, this topic has received considerable research attention and made some progress, variations, and generalizations. This paper gives a survey on the bondage number, including known results, conjectures, problems, and some comments, also selectively summarizes other types of bondage numbers.