Szczegóły publikacji
Opis bibliograficzny
Distant sum distinguishing index of graphs with bounded minimum degree / Jakub PRZYBYŁO // Ars Mathematica Contemporanea ; ISSN 1855-3966. — 2019 — vol. 17 no. 1, s. 37–49. — Bibliogr. s. 47–49, Abstr. — Publikacja dostępna online od: 2019-06-19
Autor
Słowa kluczowe
Dane bibliometryczne
| ID BaDAP | 123385 |
|---|---|
| Data dodania do BaDAP | 2019-11-05 |
| Tekst źródłowy | URL |
| DOI | 10.26493/1855-3974.1496.623 |
| Rok publikacji | 2019 |
| Typ publikacji | artykuł w czasopiśmie |
| Otwarty dostęp |  |
| Creative Commons | |
| Czasopismo/seria | Ars Mathematica Contemporanea |
Abstract
For any graph G = (V, E) with maximum degree ∆ and without isolated edges, and a positive integer r, by χ0 Σ,r(G) we denote the r-distant sum distinguishing index of G. This is the least integer k for which a proper edge colouringc: E → {1, 2, . . ., k} exists such thatP e3u c(e) 6=P e3v c(e) for every pair of distinct vertices u, v at distance at most r in G. It was conjectured that χ0 Σ,r(G) ≤ (1 + o(1))∆r− 1 for every r ≥ 3. Thus far it has been in particular proved that χ0 Σ,r(G) ≤ 6∆r− 1 if r ≥ 4. Combining probabilistic and constructive approach, we show that this can be improved to χ0 Σ,r(G) ≤ (4 + o(1))∆r− 1 if the minimum degree of G equals at least ln8 ∆. © 2019 Society of Mathematicians, Physicists and Astronomers of Slovenia. All rights reserved.
