Szczegóły publikacji
Opis bibliograficzny
On the total neighbour sum distinguishing index of graphs with bounded maximum average degree / H. Hocquard, J. PRZYBYŁO // Journal of Combinatorial Optimization ; ISSN 1382-6905. — 2020 — vol. 39 iss. 2, s. 412–424. — Bibliogr. s. 424, Abstr. — Publikacja dostępna online od: 2019-11-20
Autorzy (2)
- Hocquard Hervé
- AGHPrzybyło Jakub
Słowa kluczowe
Dane bibliometryczne
| ID BaDAP | 127245 |
|---|---|
| Data dodania do BaDAP | 2020-01-29 |
| Tekst źródłowy | URL |
| DOI | 10.1007/s10878-019-00480-4 |
| Rok publikacji | 2020 |
| Typ publikacji | artykuł w czasopiśmie |
| Otwarty dostęp |  |
| Czasopismo/seria | Journal of Combinatorial Optimization |
Abstract
A proper total k-colouring of a graph G= (V, E) is an assignment c: V∪ E→ { 1 , 2 , … , k} of colours to the edges and the vertices of G such that no two adjacent edges or vertices and no edge and its end-vertices are associated with the same colour. A total neighbour sum distinguishing k-colouring, or tnsd k-colouring for short, is a proper total k-colouring such that ∑ e ∋ uc(e) + c(u) ≠ ∑ e ∋ vc(e) + c(v) for every edge uv of G. We denote by χΣ′′(G) the total neighbour sum distinguishing index of G, which is the least integer k such that a tnsd k-colouring of G exists. It has been conjectured that χΣ′′(G)≤Δ(G)+3 for every graph G. In this paper we confirm this conjecture for any graph G with mad(G)<143 and Δ (G) ≥ 8. © 2019, Springer Science+Business Media, LLC, part of Springer Nature.
