基于特征方程的某些图双概率可靠性的统一形式

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_1p_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.

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

Suppose G=(V,E) is a graph where each vertex may independently succeed with probability p₁ when catastrophic thing happens, and each failure vertex may recovery function with independent probability p₂ where (p₁>p₂). So we definite expect of graph, and it is a polynomial of p₁ and p₂. 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.