正则q-树根图的可靠性研究

Reliability study of regular rooted q-tree

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.