超环面图上的约束数

摘要

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.%非空图G的约束数b(G)是指使得图G的控制数γ(G)增大而删除的最少的边数.[Fischermann M, Rautenbach D, Volkmann L. Remarks on the bondage number of planar graphs. Discrete Math,2003,260:57-67]已经证明,对于一个围长为g(G)的平面图G,如果g(G)≥4则b(G)≤6,如果g(G)≥5则b(G)≤5,如果g(G)≥6则b(G)≤4,如果g(G)≥8则b(G)≤3.我们把这个结果推广到连通的超环面图中.