摘要
用P(G,ρ)表示顶点完全可靠,而边则以概率ρ∈(0,1)相互独立地出现故障的图G的全终端不可靠度,即G因边故障而变得不连通的概率.本文证明了边故障率ρ充分小时,拟正则完全二部图在具有相同点数和相同边数的图类中是惟一具有最小全终端不可靠度的图.
Let P(G,ρ) denote the index of all terminal unreliability of a probabilistic graph G in which vertices are perfectly reliable while edges fail independently with a fixed probability ρ∈(0,1),that is,the probability that G becomes disconnected because of failure of some edges.This paper shows that the nearly regular complete bipartite graph Kk,k+1 uniquely attains the minimum index of all terminal unreliability over all graphs with the same order and size as Kk,k+1 when the edge failure probability ρ is sufficiently small.
出处
《高校应用数学学报（A辑）》
CSCD
北大核心
2003年第3期365-370,共6页
Applied Mathematics A Journal of Chinese Universities(Ser.A)
基金
国家自然科学基金(19971056)
浙江省自然科学基金
浙江师范大学科研基金
关键词
网络
全终端不可靠度
可靠性比较
边连通度
二阶边连通度
network
index of all terminal unreliability
reliability comparison
edge-connectivity
second edge-connectivity
