Splitting the K-Terminal Reliability

Abstract

Let G=(V,E) be a graph and K a set of terminal vertices of G. Assume that the edges of G are failing independently with given probabilities. The K-terminal reliability R(G,K) is the probability that all vertices in K are mutually connected. In this article we propose an efficient splitting formula for R(G,K) at a separating vertex set of G by lattice theoretic methods.