关于图的负对控制数的界

Bounds of Minus Paired-Domination Number in Graphs

设D V是图G=(V,E)的任意一个对控制集。如果一个函数f:V→{-1,0,1}满足条件:(1)对任意点υ∈D,有f(v)=1,对任意点v-D,有f(v)≤0;(2)对任意点v∈V,均有f(N[v])≥1;则称函数f为图G的负对控制函数。负对控制函数f的重量f(V)是v中所有点的函数值之和,图G的负对控制数γ-P(G)=min{f(V)|f是图G的负对控制函数}。本文研究了图的负对控制数的界。

Let DV be any paired-dominating set of G=(V, E), a minus paired-dominating function of G is a function of the form f:V→{-1,0,1} such that f(v)=1 for any vertex v∈D,f(v)≤0 for any vertex v∈V-D,and f(N[v])≥1 for any vertex v∈V.The weight of a minus paired-dominating function f is f(V)=Σf(v),over all vertices v∈V.The minus paired-domination number of a graph G is γ^-P(G)=min｛f(V)｜f is a minus paired-dominating function of G｝.In this paper, we obtain a few bounds of minus paired-domination number of a graph G.