Generalize activities and -terminal relia

Traldi, L., Generalized activities and K-terminal reliability, Discrete Mathematics 96 (1991) 131-149. Suppose each edge of a graph G has a given probability of being useable, and suppose K is some subset of the vertex-set of G. We present a polynomial that is useful in assessing the probability that the elements of K will lie in a particular number of components of the useable portion of G. the probability that a particular number of edges of G will be useable, and the probabilities of other properties of the useable portion of G. We also extend to this polynomial the activities analysis introduced by Tutte for his dichromatic polynomial. This leads to several expansions of this poiynomial, the standard reliability polynomial, and the K-terminal chromatic polynomial of Satyanarayana and Tindell.