Complexity to Find Wiener Index of Some Graphs

TL;DR

This paper explores the computational complexity of determining the Wiener index for specific graph classes, providing algorithms for cactus and various intersection graphs to aid in molecular structure analysis.

Contribution

It introduces algorithms for computing the Wiener index of cactus and intersection graphs, advancing methods for analyzing molecular graph properties.

Findings

Algorithms for Wiener index of cactus graphs

Algorithms for Wiener index of intersection graphs

Enhanced computational methods for molecular graph analysis

Abstract

The Wiener index is one of the oldest graph parameter which is used to study molecular-graph-based structure. This parameter was first proposed by Harold Wiener in 1947 to determining the boiling point of paraffin. The Wiener index of a molecular graph measures the compactness of the underlying molecule. This parameter is wide studied area for molecular chemistry. It is used to study the physio-chemical properties of the underlying organic compounds. The Wiener index of a connected graph is denoted by W(G) and is defined as, that is W(G) is the sum of distances between all pairs (ordered) of vertices of G. In this paper, we give the algorithmic idea to find the Wiener index of some graphs, like cactus graphs and intersection graphs, viz. interval, circular-arc, permutation, trapezoid graphs.