Petersen图类的边符号控制数

On the Edge Signed Domination Number of the Generalized Petersen Graphs

设图G=G(V,E),令函数f:E→{-1,1},f的权w(f)=∑x∈Ef[x],对x∈E中任一元素,定义f[x]=∑y∈N[x]f(y),这里N[x]表示E中x及其关联边的集合.图G的边符号控制函数为f:E→{-1,1},满足对所有的x∈E有f[x]≥1,图G的边符号控制数γS(G)就是图G上边符号控制数的最小权,称其f为图G的γS-函数.本文得到了Petersen图类的边符号控制数.

Let G=G（V,E） be a graph.For a functionf：E→{-1,1},the weight of fis w（f）=∑x∈Ef[x].For any x∈E,we define f[x]=∑y∈N[x]f（y）,where N[x] denote the edge of xand the adjacent edges of x∈E.An edge signed dominating function of G is a function f：E→{-1,1} such that f[x]≥1 for all x∈E.The edge signed domination number γS（G） of G is the minimum weight of all the edge signed dominating function on G.An edge signed dominating function of a weight γS（G） is being called γS（G）-function of G.In this paper we study the edge signed domination numbers of the Generalized Petersen graphs,and the edge signed domination number of them are obtained.