有向图的负控制数及其下界

Minus Domination Numbers and Its Lower Bounds in Directed Graphs

设D=(V,E)为一个有向图,对于函数f:V→{-1,0,1},如果对任意的v∈V,均有f(ND-[v])≥1成立,则称f为图D的一个负控制函数,图D的负控制数γ-(D)=min{w(f)|f是D一个负控制函数}.给出几类有向图的负控制数的值,并得到一般有向图的负控制数的几个下界.

Let D=（V,A） be a digraph. For a functionf：V（D）→{-1,0,1} ,if f（N [v]）≥1 for each vertex v∈V, then f is called a minus dominating function on D. The minus domination number T-（D） = min{w（f）[ f is a minus domi- nating function on D}. The minus domination numbers were given for a few types of digraphs. And some lower bounds were obtained for minus domination number of general digraphs.