On Bondage Numbers of Graphs: A Survey with Some Comments. (13th May 2013)

• Record Type: Journal Article
• Authors: Xu, Jun-Ming
• Other Names: Hoang Chính T. Academic Editor.
• Is Part Of: International journal of combinatorics. Volume 2013(2013)
• Publication Date: 2013-05-13
• Subjects: Combinatorial analysis -- Periodicals; Combinatorial analysis; Periodicals; Electronic journals; 511.605
• DOI: 10.1155/2013/595210
• Languages: English
• ISSNs: 1687-9163

Abstract

Abstract : The domination number of a graphG is the smallest number of vertices which dominate all remaining vertices by edges ofG . The bondage number of a nonempty graphG is the smallest number of edges whose removal fromG results in a graph with domination number greater than the domination number ofG . 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.