Elsevier

Discrete Mathematics

Volume 308, Issue 23, 6 December 2008, Pages 5446-5453
Discrete Mathematics

Restrained bondage in graphs

https://doi.org/10.1016/j.disc.2007.10.016Get rights and content
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Abstract

Let G=(V,E) be a graph. A set SV is a restrained dominating set if every vertex not in S is adjacent to a vertex in S and to a vertex in VS. The restrained domination number of G, denoted by γr(G), is the smallest cardinality of a restrained dominating set of G. We define the restrained bondage number br(G) of a nonempty graph G to be the minimum cardinality among all sets of edges EE for which γr(GE)>γr(G). Sharp bounds are obtained for br(G), and exact values are determined for several classes of graphs. Also, we show that the decision problem for br(G) is NP-complete even for bipartite graphs.

Keywords

Restrained domination
Bondage number
Restrained bondage

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