基于特征方程的某些图双概率可靠性的统一形式

Uniform Form of Some Graphs' Two Probability Reliability Based on Characteristic Equation

设灾难发生时,图G=(V,E)的各顶点以独立概率p_1幸存,失效的顶点灾后以概率p2独立恢复功能(p_1>p_2).定义了双概率可靠性,利用减缩边递推公式得到路图、正则q-树和圈图的迭代式满足二阶特征方程,并利用它们各自的初值,计算得到它们的统一形式的通项表达式.

Suppose G=(V,E)is a graph where each vertex may independently succeed with probability p 1 when catastrophic thing happens,and each failure vertex may recovery function with independent probability p 2 where(p 1>p 2).So we definite expect of graph,and it is a polynomial of p 1 and p 2.And expect is a proper index of reliability.By means of deletion contraction edge formula,we have found that path graph,regular q-tree graph and cycle graph satisfy the second order characteristic equation.So we can calculate the coefficients with its initial value,and then the uniform form of general term is obtained.