Bicyclic Graphs with the Second Up to Seventh Largest Wiener Indices

Abstract

The Wiener index of a connected graph is the sum of distances between all pairs of vertices in the graph. Feng et al. in [The hyper-Wiener index of bicyclic graphs, Utilitas Math., \(84(2011) 97-104\)] determined the bicyclic graphs having the largest Wiener index. In this article, we determine the graphs having the second up to seventh largest Wiener indices among all bicyclic graphs with \(n\) vertices.