Note on calculating Wiener numbers of molecular graphs with symmetry (Q1807870)

The Wiener number \(W\) of a molecular graph with vertex set \(V\) is defined by \[ W= \sum_{(u,v)\subseteq V} d(u,v), \] where \(d(u,v)\) is the graph-theoretical distance between \(u\) and \(v\). In an earlier paper [Match 35, 213-226 (1997)], the authors gave a simple method for calculating \(W\) when the graph has symmetry. The present paper improves and simplifies such calculations.