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根图的稳定性及其优化
引用本文:王冰杰[] 、唐晓清[]. 根图的稳定性及其优化[J]. 西南师范大学学报(自然科学版), 2017, 42(4)
作者姓名:王冰杰[] 、唐晓清[]
作者单位:白城师范学院数学与统计学院,吉林 白城,137000 ; 上海立信会计金融学院统计与数学学院,上海,201620
基金项目:吉林省自然科学项目,吉林省教育科学"十二五"规划重点自助课题
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.

关 键 词:根图   可靠性   稳定性   减-缩边公式   期望-方差优化

On Stability of Rooted Graph and Its Optimality
WANG Bing-jie[],TANG Xiao-qing[]. On Stability of Rooted Graph and Its Optimality[J]. Journal of southwest china normal university(natural science edition), 2017, 42(4)
Authors:WANG Bing-jie[]  TANG Xiao-qing[]
Abstract: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 E2(G;p), which is the expect of vertices number square, then variance D(G;p)=E2(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.
Keywords:
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