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On the relationship between variable Wiener index and variable Szeged index
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Cambie, Stijn and Haslegrave, John (2022) On the relationship between variable Wiener index and variable Szeged index. Applied Mathematics and Computation, 431 . 127320. doi:10.1016/j.amc.2022.127320 ISSN 0096-3003.
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Official URL: https://doi.org/10.1016/j.amc.2022.127320
Abstract
We resolve two conjectures of Hriňáková et al. (2019) concerning the relationship between the variable Wiener index and variable Szeged index for a connected, non-complete graph, one of which would imply the other. The strong conjecture is that for any such graph there is a critical exponent in (0,1], below which the variable Wiener index is larger and above which the variable Szeged index is larger. The weak conjecture is that the variable Szeged index is always larger for any exponent exceeding 1. They proved the weak conjecture for bipartite graphs, and the strong conjecture for trees.
In this note we disprove the strong conjecture, although we show that it is true for almost all graphs, and for bipartite and block graphs. We also show that the weak conjecture holds for all graphs by proving a majorization relationship.
Item Type: | Journal Article | |||||||||
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Subjects: | Q Science > QA Mathematics | |||||||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | |||||||||
SWORD Depositor: | Library Publications Router | |||||||||
Library of Congress Subject Headings (LCSH): | Graph theory, Topological algebras | |||||||||
Journal or Publication Title: | Applied Mathematics and Computation | |||||||||
Publisher: | Elsevier BV | |||||||||
ISSN: | 0096-3003 | |||||||||
Official Date: | 15 October 2022 | |||||||||
Dates: |
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Volume: | 431 | |||||||||
Article Number: | 127320 | |||||||||
DOI: | 10.1016/j.amc.2022.127320 | |||||||||
Status: | Peer Reviewed | |||||||||
Publication Status: | Published | |||||||||
Access rights to Published version: | Open Access (Creative Commons) | |||||||||
Date of first compliant deposit: | 13 July 2022 | |||||||||
Date of first compliant Open Access: | 13 July 2022 | |||||||||
RIOXX Funder/Project Grant: |
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