几类图弱控制的广义束缚数  

THE GENERAL BONDAGE NUMBER OF WEAK DOMINATION FOR SOME GRAPHS

作　　者：吴亚平[1] 王芳[1] 范琼[1] 毛经中[1] 

机构地区：[1]华中师范大学数学与统计学院,武汉430079

出　　处：《经济数学》2004年第3期267-271,共5页Journal of Quantitative Economics

基　　金：获教育部科学技术研究重点项目资助 (批准号 :0 2 139)

摘　　要：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.

关 键 词：弱控制 弱控制的广义束缚数 弱控制的去边临界图 

分 类 号：F22[经济管理—国民经济]