几类图弱控制的广义束缚数

THE GENERAL BONDAGE NUMBER OF WEAK DOMINATION FOR SOME GRAPHS

对任一图 G,其弱控制的束缚数 ,广义束缚数分别定义为 :bw(G) =min{ | E‖ E E(G) ,且 γw(G- E)>γw(G) } .b w(G) =min{ t| E E(G) ,如果 | E| =t,则有γw(G- E) >γw(G) } .在本文中我们给出了几类图的弱控制的广义束缚数的精确值 ,称 b w(G) =1图为弱控制去边临界图 ,并研究了正则图是弱控制去边临界图的充要条件 ,以及一般图和树的必要条件 .

For any graph G,the bondage number of γ w,b w(G) is defined to be the minumum cardinality of a set of edges whose removel from G results in a graph G satisfying γ w(G)>γ w(G). the general bondage number of γ w,b w(G) is defined to be the minumum cardinality of every arbitrary set of edges whose removal from G results in graph G satisfying γ w(G) >γ w(G).We give exact values of b w(G) for some classes of graphs.And we consider the special case of b w(G),that b w(G) is equal to 1,we call G is edge-removal-critical(ER-critical).Then give necessary and sufficient condition for regular graphs to be ER-critical and necessary conditon for a tree to be ER-critical.