The maximum Wiener index of a uniform hypergraph

TL;DR

This paper determines the maximum Wiener index for connected n-vertex k-uniform hypergraphs and characterizes all hypergraphs that achieve this maximum, advancing understanding of hypergraph distance metrics.

Contribution

It provides a precise maximum Wiener index for connected k-uniform hypergraphs and characterizes all hypergraphs attaining this maximum.

Findings

Maximum Wiener index for connected n-vertex k-uniform hypergraphs identified

Characterization of all hypergraphs with maximum Wiener index provided

Theoretical bounds established for hypergraph Wiener indices

Abstract

The Wiener index of a (hyper)graph is calculated by summing up the distances between all pairs of vertices. We determine the maximum possible Wiener index of a connected $n$-vertex $k$-uniform hypergraph and characterize for every~$n$ all hypergraphs attaining the maximum Wiener index.