Some results on the Wiener index related to the Soltes problem of graphs Full article
| Journal |
Discrete Applied Mathematics
ISSN: 0166-218X |
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| Output data | Year: 2024, Volume: 344, Pages: 154-160 Pages count : 7 DOI: 10.1016/j.dam.2023.11.041 | ||||
| Tags | Wiener index, Šoltés problem | ||||
| Authors |
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| Affiliations |
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Funding (1)
| 1 | Russian Science Foundation | 23-21-00459 |
Abstract:
The Wiener index, W(G), of a connected graph G is the sum of distances between its vertices. In 2021, Akhmejanova et al. posed the problem of finding graphs G with large Rm(G) = |{v ∈ V (G) |W(G) − W(G − v) = m ∈ Z}|/|V (G)| for any integer m ≥ 0. It is shown that there is a graph G with Rm(G) > 1/2 for any m ≥ 0. In particular, there is a regular graph of even degree with this property for any odd m ≥ 1. The proposed approach allows to construct new families of graphs G with R0(G) → 1/2 when the order of G increases.
Cite:
Dobrynin A.A.
, Vorob’ev K.V.
Some results on the Wiener index related to the Soltes problem of graphs
Discrete Applied Mathematics. 2024. V.344. P.154-160. DOI: 10.1016/j.dam.2023.11.041 WOS Scopus РИНЦ OpenAlex
Some results on the Wiener index related to the Soltes problem of graphs
Discrete Applied Mathematics. 2024. V.344. P.154-160. DOI: 10.1016/j.dam.2023.11.041 WOS Scopus РИНЦ OpenAlex
Dates:
| Submitted: | Apr 26, 2023 |
| Accepted: | Nov 23, 2023 |
| Published online: | Dec 27, 2023 |
| Published print: | Feb 15, 2024 |
Identifiers:
| Web of science: | WOS:001127792200001 |
| Scopus: | 2-s2.0-85178346596 |
| Elibrary: | 64925859 |
| OpenAlex: | W4389066992 |