The least Euclidean distortion constant of a distance-regular graph
| العنوان: | The least Euclidean distortion constant of a distance-regular graph |
|---|---|
| المؤلفون: | Sebastian M. Cioabă, Himanshu Gupta, Ferdinand Ihringer, Hirotake Kurihara |
| بيانات النشر: | arXiv, 2021. |
| سنة النشر: | 2021 |
| مصطلحات موضوعية: | Applied Mathematics, FOS: Mathematics, Mathematics - Combinatorics, Discrete Mathematics and Combinatorics, Combinatorics (math.CO) |
| الوصف: | In 2008, Vallentin made a conjecture involving the least distortion of an embedding of a distance-regular graph into Euclidean space. Vallentin's conjecture implies that for a least distortion Euclidean embedding of a distance-regular graph of diameter $d$, the most contracted pairs of vertices are those at distance $d$. In this paper, we confirm Vallentin's conjecture for several families of distance-regular graphs. We also provide counterexamples to this conjecture, where the largest contraction occurs between pairs of vertices at distance $d{-}1$. We suggest three alternative conjectures and prove them for several families of distance-regular graphs. Comment: 19 pages |
| DOI: | 10.48550/arxiv.2109.09708 |
| URL الوصول: | https://explore.openaire.eu/search/publication?articleId=doi_dedup___::b6e9af2b3b6a741929b84dd81048f771 |
| Rights: | OPEN |
| رقم الانضمام: | edsair.doi.dedup.....b6e9af2b3b6a741929b84dd81048f771 |
| قاعدة البيانات: | OpenAIRE |
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