one of the generalizations of the wiener number to weighted graphs is to assign probabilities to edges, meaning that in nonstatic conditions the edge is present only with some probability. the reliability wiener number is defined as the sum of reliabilities among pairs of vertices, where the reliability of a pair is the reliability of the most reliable path. closed expressions are derived for t...

One of the generalizations of the Wiener number to weighted graphs is to assign probabilities to edges, meaning that in nonstatic conditions the edge is present only with some probability. The Reliability Wiener number is defined as the sum of reliabilities among pairs of vertices, where the reliability of a pair is the reliability of the most reliable path. Closed expressions are derived for t...

reliability wiener number is a modification of the original wiener number in which probabilities are assigned to edges yielding a natural model in which there are some (or all) bonds in the molecule that are not static. various probabilities naturally allow modelling different types of chemical bonds because chemical bonds are of different types and it is well-known that under certain condition...

Reliability Wiener number is a modification of the original Wiener number in which probabilities are assigned to edges yielding a natural model in which there are some (or all) bonds in the molecule that are not static. Various probabilities naturally allow modelling different types of chemical bonds because chemical bonds are of different types and it is well-known that under certain condition...

Recently various generalizations or extensions of the now “classical” Wiener number1 have become of interest, both as regards new individual numbers2-7 and as regards sequences of numbers.8-12 Of particular interest here are those numbers of Tratch et al.2 and of Randić,3 their manner of interrelation, their formulas for trees as extended to general cycle-containing graphs, and their extension ...

The aim of this paper is to study the global reliability of communication networks. We assume that, in a communication network, the weights of the edges quantify the volume or the quality of the information transmitted by the nodes. In such a case, the strength of a path (resp. walk), called the reliability of the path (resp. walk) can be calculated as the product of the weights of the edges be...