- Tytuł:
- An Improved Upper Bound on Neighbor Expanded Sum Distinguishing Index
- Autorzy:
- Vučković, Bojan
- Powiązania:
- https://bibliotekanauki.pl/articles/32083737.pdf
- Data publikacji:
- 2020-02-01
- Wydawca:
- Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
- Tematy:
-
general edge coloring
total coloring
neighbor sum distinguishing index - Opis:
- A total k-weighting f of a graph G is an assignment of integers from the set {1, . . ., k} to the vertices and edges of G. We say that f is neighbor expanded sum distinguishing, or NESD for short, if Σw∈N(v) (f(vw) + f(w)) differs from Σw∈N(u)(f(uw) + f(w)) for every two adjacent vertices v and u of G. The neighbor expanded sum distinguishing index of G, denoted by egndiΣ(G), is the minimum positive integer k for which there exists an NESD weighting of G. An NESD weighting was introduced and investigated by Flandrin et al. (2017), where they conjectured that egndiΣ(G) ≤ 2 for any graph G. They examined some special classes of graphs, while proving that egndiΣ(G) ≤ χ(G) + 1. We improve this bound and show that egndiΣ(G) ≤ 3 for any graph G. We also show that the conjecture holds for all bipartite, 3-regular and 4-regular graphs.
- Źródło:
-
Discussiones Mathematicae Graph Theory; 2020, 40, 1; 323-329
2083-5892 - Pojawia się w:
- Discussiones Mathematicae Graph Theory
- Dostawca treści:
- Biblioteka Nauki
Artykuł