图的k符号边控制数

设G=(V,E)是一个图,一个函数f:E→{-1,+1},如果对于G中至少k条边e有sum from e'∈Ne]f(e')≥1成立,则称f为图G的一个k符号边控制函数.一个图的k符号边控制数定义为γ_(ks)^/(G)=min{∑_(e∈E(G))f(e)|f为图G的一个k符号边控制函数}.主要给出了一个图G的k符号边控制数γ_(ks)/(G)=min{∑_(e∈E(G))f(e)|f为图G的一个k符号边控制函数}.主要给出了一个图G的k符号边控制数γ_(ks)^/(G)的若干新下限,并确定了路和圈的k符号边控制数.

k Signed Edge Domination Numbers in Graphs

Let G =(V,E)be a graph,a function f:E→{-1,1} is said to be the k signed edge dominating function of G if sum from e'∈N(e)f(e')≥1holds for at least k edges e G E(G).The k signed edge domination numberγ_(ks)~/(G)of Gis defined asγ_(ks)~/(G)=min{Σ_(e∈E(G)) f(e)|f is a k signed edge dominating function of G}.In this paper we mainly give some new lower bounds of the k signed edge domination numberγ_(ks)~/(G)of a graphG,and get the k signed edge domination number for the paths and the cycles.