A sharp lower bound for the Wiener index of a graph

TL;DR

This paper establishes a precise lower bound for the Wiener index of any connected graph based on its order, size, and diameter, providing insights relevant to molecular graph analysis.

Contribution

It introduces a new sharp lower bound for the Wiener index of arbitrary graphs using their fundamental parameters.

Findings

Derived a sharp lower bound for W(G) in terms of order, size, and diameter.

Applicable to molecular graphs in chemistry.

Enhances understanding of graph distance metrics.

Abstract

Given a simple connected undirected graph G, the Wiener index W(G) of G is defined as half the sum of the distances over all pairs of vertices of G. In practice, G corresponds to what is known as the molecular graph of an organic compound. We obtain a sharp lower bound for W(G) of an arbitrary graph in terms of the order, size and diameter of G.