摘要
设灾难发生时,根图G的边以概率p独立幸存,则含根连通子图的顶点数的期望值EV(G;p)是根图的可靠性的合适指标.定义了子图的顶点数的平方期望值E2(G;p)后,则方差D(G;p)=E2(G;p)-[EV(G;p)]~2是根图稳定性的合适指标.推导得到了E2(G;p)的减-缩边公式,从而得到方差的一个递归计算方法.进而研究了一些特殊图的方差的计算公式.最后,结合期望和方差,讨论了根图的优化问题.
When G is a rooted graph where each edge may independently succeed with probability p when catastrophic thing happens, we consider the expected number of vertices in the operational component of G containing the root. Then the expected value of edges number EV （, G ; p ） is a proper index of reliability to rooted graph. Later, we give the definition E 2（G ; p ） , which is the expect of vertices number square, then variance D （G; p ） = E 2（G; p ） - [EV （G; p ）^2. Especially, we get the deletion-contraction edge formula of E2（G ; p）. So we obtain a recursive computing variance method. And D （G; p ） is a proper stability index to the rooted graph. With this formula, we get some variance computational formulas of specific rooted graphs. Finally, we propose expect-variance optimality of rooted graph.
作者
王冰杰
唐晓清
WANG Bing-jie TANG Xiao-qing(School of Mathematics and Statistics, Baicheng Normal University,Baicheng Jilin 137000 , China , School of Statistics ＆ Mathematics, Shanghai Lixin University of Accounting and Finance,Shanghai 201620 , China)
出处
《西南师范大学学报（自然科学版）》
CAS
北大核心
2017年第4期14-19,共6页
Journal of Southwest China Normal University(Natural Science Edition)
基金
吉林省自然科学项目(20101564)
吉林省教育科学"十二五"规划重点自助课题(ZC12069)
关键词
根图
可靠性
稳定性
减-缩边公式
期望-方差优化
rooted graph
reliability
stability
deletion-contraction edge formula
expect-variance optimality
