图的Fractional边控制与Fractional边全控制

On Fractional Edge Total Domination of Graphs

设G=(V,E)是一个图,一个函数f:E→[0,1]如果对所有的边e∈E(G),都有∑e∈N(e')f(e)≥1成立,则称f为图G的一个Fractional边全控制函数,简记为F边全控制函数,此处N(e')表示G中与边e'相关联的边集。图G的F边全控制数定义为γ'tf(G)=min{∑e∈E(G)f(e)f是G的一个F边全控制函数}.本文得到了一般图的F边全控制数的若干界限,还确定了一些特殊图的F边全控制数。

Let G=（V,E）be a graph,a functionf：E→ is said to be the fractional edge total dominating function（F edge total dominating function in brief） of Gif ∑e∈N（e′）f（e）≥1holds for every edge e∈E（G）.The fractional edge total domination number of G is defined as γ′tf（G）=min{∑e∈E（G）f（e）│f is aFETDFof G.} In this paper,we give some bounds of the fractional edge total domination numbers of graphs,and determine the fractional edge domination numbers and fractional edge total domination numbers of some special graphs.