A variety of probabilistic notions of network reliability of graphs and digraphs have been
proposed and studied since the early 1950s. Although grounded in the engineering and …

The aim of this paper is to give a characterization of the set of roots of a special family of
polynomials. This family is relevant in reliability theory since it contains the reliability …

Given a graph G whose edges are perfectly reliable and whose nodes each operate
independently with probability p∈[0, 1], the node reliability of G is the probability that at least …

The node reliability of a graph G is the probability that at least one node is operational and
that the operational nodes can all communicate in the subgraph that they induce, given that …

Suppose we have a graph G (finite and undirected) where the vertices of G are always
operational, but the edges of G operate independently with probability. The all‐terminal …

Edge reliability problem has many applications in different field of science and engineering
such as: cognitive science, neuroscience, electrical engineering, network science and so on …

Given a connected graph $ G $ whose vertices are perfectly reliable and whose edges each
fail independently with probability $ q\in [0, 1], $ the\textit {(all-terminal) reliability} of $ G $ is …

The Tutte polynomial is surely the most studied graph polynomial, particularly when all of its
many specializations, generalizations, and applications are included. The impact of the Tutte …

Given a connected graph G whose vertices are perfectly reliable and whose edges each fail
independently with probability q∈[0, 1], the (all‐terminal) reliability of G is the probability that …