On bondage number of toroidal graphs
Xirong Xu · 2009
The bondage number b(G) of a nonempty graph G is the cardinality of a smallest edge set whose removal from G results in a graph with the domination number greater than the domination number γ(G) of G.[Fischermann M,Rautenbach D,Volkmann L.Remarks on the bondage number of planar graphs.Discrete Math,2003,260:57-67] showed that for a connected planar graph G with girth g(G),b(G)≤6 if g(G)≥4,b(G)≤5 if g(G)≥5,b(G)≤4 if g(G)≥6 and b(G)≤3 if g(G)≥8.This result was generalized to a connected toroidal graph that was embeddable on the torus.