Szczegóły publikacji
Opis bibliograficzny
Distant irregularity strength of graphs with bounded minimum degree / Jakub PRZYBYŁO // Discrete Applied Mathematics ; ISSN 0166-218X. — 2017 — vol. 233, s. 159–165. — Bibliogr. s. 165, Abstr. — Publikacja dostępna online od: 2017-09-29
Autor
Słowa kluczowe
Dane bibliometryczne
| ID BaDAP | 110083 |
|---|---|
| Data dodania do BaDAP | 2017-12-08 |
| Tekst źródłowy | URL |
| DOI | 10.1016/j.dam.2017.08.011 |
| Rok publikacji | 2017 |
| Typ publikacji | artykuł w czasopiśmie |
| Otwarty dostęp |  |
| Czasopismo/seria | Discrete Applied Mathematics |
Abstract
Consider a graph G = (V, E) without isolated edges and with maximum degree Delta. Given a colouring c : E -> {1, 2, ..., k} the weighted degree of a vertex v is an element of V is the sum of its incident colours, i.e., Sigma(e(sic)v)c(e). For any integer r >= 2, the least k admitting the existence of such c attributing distinct weighted degrees to any two different vertices at distance at most r in G is called the r -distant irregularity strength of G and denoted by s(r)(G). This graph invariant provides a natural link between the well known 1-2-3 Conjecture and irregularity strength of graphs. In this paper we apply the probabilistic method in order to prove an upper bound s(r)(G) <= (4 + o(1))Delta(r-1) for graphs with minimum degree delta >= ln(8) Delta, improving thus far best upper bound s(r)(G) <= 6 Delta(r-1).
