关于图的反符号圈控制数

摘要：引入了图的反符号圈控制的概念，设G=（V，E）是一个非空图，一个函数f：E→{＋1，-1}对G中每一个无弦圈C均有∑e∈E（G）f（e）≤0成立，则称厂为图G的一个反符号圈控制函数，而γ′rsc（G）=max{∑e∈E（G）f（e）｜f为图G的反符号圈控制函数｜称为图G的反符号圈控制数。给出了图的反符号圈控制数的界限，刻画了满足γ′rsc（G）=-｜E（G）｜＋2的所有连通图G，并且确定了图与补图以及几类特殊图的反符号圈控制数。

On Reverse Signed Cycle Domination in Graphs

We introduce the concept of reverse signed cycle domination in graphs. Let G = （V,E） be a non-empty graph, a functionf：E→{＋1,-1} is said to be a reverse signed cycle domination function （RSCDF） of G if ∑e∈E（G）f（e）≤0 holds for any induced cycle C of G, and γ′rsc（G）=max{∑e∈E（G）f（e）｜fis an RSCDF of G ｜ is called the reverse signed cycle domination number of G. We obtain bounds of γ′rsc（G）, characterize all connected graphs G with γ′（G） =-｜E（G） }＋2, and determine the exact values of reverse signed cycle domination number for a graph and its complement and some special classes of graphs.