On the reliability of a number of s-p reducible graphs

Let G=(V,E) be a graph whose edges may fail with known probabilities and let K a subset of V be specified. The overall reliability of G, denoted by R(G), is the probability that all vertices in K=V communicate with each other. We have two types of graphs, s-p reducible and s-p complex, depending on whether after series-arallel reductions the result is a single edge or not. A number of s-p reducible graphs are presented and expressions that evaluate their overall reliability are introduced.