Upper bounds on the bondage number of a graph

Vladimir Dimitrov Samodivkin (Departments of Mathematics, University of Architecture, Civil Engineering and Geodesy, Sofia, Bulgaria)

Electronic Journal of Graph Theory and Applications (EJGTA)
Vol 6, No 1 (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 having domination number at least four. Several unanswered questions are posed.