A NOTE: RELATION BETWEEN TOTAL VERTEX STRESS AND WIENER INDEX

Abstract

This note introduces results in respect of a relation between the total vertex stress and the Wiener index of a graph. In respect of the total vertex stress \(S(G)\) and the Wiener index \(W(G)\) of a non-trivial geodetic graph, it is established that \(W(G)=S(G)+\binom{n}{2}\). The aforesaid holds for even cycles and uni-Joost graphs as well. Avenues for further research are also suggested.