Upper bounds on the bondage number of a graph

Vladimir Dimitrov Samodivkin
2018 Electronic Journal of Graph Theory and Applications  
The bondage number b(G) of a graph G is the smallest number of edges whose removal from G results in a graph with larger domination number. We obtain sufficient conditions for the validity of the inequality b(G) ≤ 2s − 2, provided G has degree s vertices. We also present upper bounds for the bondage number of graphs in terms of the girth, domination number and Euler characteristic. As a corollary we give a stronger bound than the known constant upper bounds for the bondage number of graphs
more » ... mber of graphs having domination number at least four. Several unanswered questions are posed.
doi:10.5614/ejgta.2018.6.1.1 fatcat:6ohhgnnxb5gs7hblypg4j2xomu