On the main distance-based entropies: the eccentricity- and Wiener-entropy
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arXiv
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866909427456540672 |
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| author | Cambie, Stijn Dong, Yanni |
| author_facet | Cambie, Stijn Dong, Yanni |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2208_12209 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | On the main distance-based entropies: the eccentricity- and Wiener-entropy Cambie, Stijn Dong, Yanni Combinatorics 05C12, 05C09, 05C35, 94A17 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. |
| title | On the main distance-based entropies: the eccentricity- and Wiener-entropy |
| topic | Combinatorics 05C12, 05C09, 05C35, 94A17 |
| url | https://arxiv.org/abs/2208.12209 |