Note on "A Linear-Time Algorithm for Computing K-Terminal Reliability in a Series-Parallel Network"

In an original and very interesting paper (Satyanarayana and Wood [1]) concerning polygon-to-chain reductions in a stochastic network, a small inconsistency occurs in the proof of Theorem 1. In particular, this happens in cases where the whole set of {\bit K}-vertices lies in the remaining polygon. Such an example is the case of polygon type 5, where the appropriate note has been made by the authors for $|\hbox{\bit K}| = 2$. Analogous notes must also be made for polygon types 4, 6, and 7, when {\bit K}$ = 2$, 3, and 4, respectively. The correct transformations are given in Table 1 (note that dark vertices are {\bit K}-vertices).