The bondage numbers of graphs with small crossing numbers

The bondage number b(G)b(G) of a nonempty graph G is the cardinality of a smallest edge set whose removal from G   results in a graph with domination number greater than the domination number γ(G)γ(G) of G  . Kang and Yuan proved b(G)⩽8b(G)⩽8 for every connected planar graph G. Fischermann, Rautenbach and Volkmann obtained some further results for connected planar graphs. In this paper, we generalize their results to connected graphs with small crossing numbers.