Bondage number of planar graphs Original Research Article

The bondage number b(G) of a nonempty graph G is the cardinality of a smallest set of edges whose removal from G results in a graph with a domination number greater than the domination number of G. In this paper, we prove that b(G)⩽min {8,Δ(G)+2} for a planar graph G and b(G)⩽3 for a graph G with forbidden minor K4.