Partitions and network reliability

The all-terminal reliability and K-terminal reliability of networks are oft en considered as separate problems. We use the partition lattice of the ver tex set of an undirected graph to show that these reliability measures are closely related. As an application of the presented approach, a formula for the K-terminal reliability polynomial of the complete graph and Buzacott's node partition formula are derived. (C) 1999 Elsevier Science B.V. All rig hts reserved.