Szczegóły publikacji
Opis bibliograficzny
Distant sum distinguishing index of graphs / Jakub PRZYBYŁO // Discrete Mathematics ; ISSN 0012-365X. — 2017 — vol. 340 iss. 10, s. 2402–2407. — Bibliogr. s. 2406–2407, Abstr.
Autor
Słowa kluczowe
Dane bibliometryczne
| ID BaDAP | 109370 |
|---|---|
| Data dodania do BaDAP | 2017-10-19 |
| Tekst źródłowy | URL |
| DOI | 10.1016/j.disc.2017.05.009 |
| Rok publikacji | 2017 |
| Typ publikacji | artykuł w czasopiśmie |
| Otwarty dostęp |  |
| Czasopismo/seria | Discrete Mathematics |
Abstract
Consider a positive integer r and a graph G = (V, E) with maximum degree Delta and without isolated edges. The least k so that a proper edge colouring c : E -> 1, 2,..., k} exists such that Sigma(c(e))(e there exists u) not equal Sigma(e there exists u)c(e) for every pair of distinct vertices u, vat distance at most r in G is denoted by x'(Sigma,r) (G). For r = 1, it has been proved that x'(Sigma,1)(G) = (I + o(1))Delta. For any r >= 2 in turn an infinite family of graphs is known with x'(Sigma,r)(G) = Omega(Delta(r-1)). We prove that, on the other hand,)(1.E,r(G) = O(Delta(r-1)) for r >= 2. In particular, we show that x'(Sigma,r)(G) <= 6A(r-1) if r >= 4.