图的符号星k控制数

引入了图的符号星k控制的概念.设G=（V,E）是一个图,一个函数f：E→{-1,＋1},如果∑e∈Ev]f（e）≥1对于至少k个顶点v∈V（G）成立,则称f为图G的一个符号星k控制函数,其中E（v）表示G中与v点相关联的边集.图G的符号星k控制数定义为γkss（G）=min{∑e∈Ef（e）｜f为图G的符号星k控制函数}.在本文中,我们主要给出了一般图的符号星k控制数的若干下界,推广了关于符号星控制的一个结果,并确定路和圈的符号星k控制数.

On signed star k domination numbers of graphs

In this paper,we introduce the concept of signed star k domination in graphs. Let G = (V,E) be a graph,a function f : E→{-l,+1}is said to be a signed star k dominating function (SSkDF) of G if ∑_(e∈Ev])f(e)≥1 holds for at least k vertices v ∈V,where E(v) denotes the set of edges incident with v. The signed star k domination number of is defined as γ_(ss)~κ(G)=min{∑_(e∈Ef)(e)|f is an SSkDF of G}. In this paper we obtain some lower bounds of γ_(ss)~κ(G) for general graphs G,generalize a result about the signed star domination,and determine the signed star k domination numbers for the path and cycle of order n .