University of KashanIranian Journal of Mathematical Chemistry2228-64895220141101On the Reliability Wiener Number107118737710.22052/ijmc.2014.7377ENDarja Rupnik PoklukarUniversity of LjubljanaJanez ZerovnikUniversity of LjubljanaJournal Article20140417One 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 the Reliability Wiener number of paths, cycles, stars and brooms. It is shown that the Reliability Wiener number can be used as a measure of branching.https://ijmc.kashanu.ac.ir/article_7377_5ee148bffddfb55795e543f75ea1b00d.pdf