有向图的k-彩虹控制数的界

摘要

设γrk(D)是有向图D的后-彩虹控制数.用构造的方法得到有向图的后-彩虹控制数的一些上下界,这些界与图的顶点数、最大出度、罗马控制数等密切相关;给出γrk(D)=k的充分必要条件,利用概率方法得到了有向图的后-彩虹控制数的一个上界.%Let γrk (D) be the k-rainbow domination number of a digraph D.The upper and lower bounds on the k-rainbow domination number of digraphs are found by construction methods,which are closely related to the number of vertices,maximum out-degree,Roman domination number,etc.And the sufficient and necessary conditions of γrk (D) =k are given.Moreover,an upper bound on the k-rainbow domination number of digraphs is found by probability method.