摘要
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.
出处
《宜春学院学报》
2010年第4期8-9,共2页
Journal of Yichun University
关键词
图
Petersen图类
边符号控制数
边符号控制函数
Graph
the Generalized Petersen graphs
the Edge Signed Dominating Function
the Edge Signed