On the main distance-based entropies: the eccentricity- and Wiener-entropy

Stijn Cambie; Yanni Dong

On the main distance-based entropies: the eccentricity- and Wiener-entropy

Combinatorics 2024-12-17 v3

Authors: Stijn Cambie , Yanni Dong

Abstract

We define the Wiener-entropy, which is together with the eccentricity-entropy one of the most natural distance-based graph entropies. By deriving the (asymptotic) extremal behaviour, we conclude that the Wiener-entropy of graphs of a given order is more spread than is the case for the eccentricity-entropy. We solve $3$ conjectures on the eccentricity-entropy and give a conjecture on the Wiener-entropy related to some surprising behaviour on the graph minimizing it.

Keywords

wiener-entropy eccentricity-entropy graph entropy distance-based entropy extremal behavior graph conjectures

Cite

@article{arxiv.2208.12209,
  title  = {On the main distance-based entropies: the eccentricity- and Wiener-entropy},
  author = {Stijn Cambie and Yanni Dong},
  journal= {arXiv preprint arXiv:2208.12209},
  year   = {2024}
}

Comments

16 pages, 4 figures, 3 tables v2: computer verifications have been added

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