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The maximum Wiener index of a uniform hypergraph

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arxiv 2302.08686 v1 pith:OJMNVMW2 submitted 2023-02-17 math.CO

Stijn Cambie , Ervin Győri , Nika Salia , Casey Tompkins , James Tuite This is my paper · ORCID
classification math.CO
keywords indexwienermaximumhypergraphuniformattainingcalculatedcharacterize
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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.

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  1. Uniform \v{S}olt\'es' hypergraphs and \v{S}olt\'es' weighted graphs

    math.CO 2025-06 conditional novelty 7.0 of 10

    Uniform Šoltés' hypergraphs first occur at order 10, exist for every order n >= 10 and most uniformities k >= 4, a non-regular 9-uniform example exists, and infinitely many weighted Šoltés' graphs exist.

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