正则q-树根图的可靠性研究  

Reliability study of regular rooted q-tree

作　　者：刘莹[1] 唐晓清[2] 

机构地区：[1]邵阳学院理学与信息科学系,湖南邵阳422000 [2]上海立信会计学院数学与信息学院,上海201620

出　　处：《东北师大学报（自然科学版）》2015年第1期17-21,共5页Journal of Northeast Normal University(Natural Science Edition)

基　　金：国家自然科学基金资助项目(60872060)

摘　　要：对根图的顶点的幸存概率进行了期望值研究,得出一个重要的定理,即减-缩边公式.由此,得到一些特殊根图的期望值计算公式及正则q-树根图和正则q-树整子根图的期望值计算公式.讨论了根图的均值和方差的后验计算公式,以及整体优化的思路.Expected value is a key index of rooted graph reliability.We propose a new vertex surviving rooted graph,that is,when Gis a rooted graph where each vertex may independently succeed with probability p when catastrophic thing happens,we consider the expected number of edges in the operational component of G containing the root.And we get a very important and useful compute formula which is deletion-contraction formula.By using this formula,we get some specific graphs＇expected value calculate formulas.Then,we study regular rooted q-tree and integral subgraph of regular rooted q-tree,we get the compute formulas of them.Later,we discuss the mean and variance of expected value when the parameter p has prior distribution.Finally,we discuss the optimality of rooted graph,that is,we propose mean-variance optimality idea for further discussion.

关 键 词：根图 期望值 正则q-树根图 正则q-树整子根图 均值-方差优化 

分 类 号：O157.5[理学—数学]