Neighbor Sum Distinguishing Index - Inria - Institut national de recherche en sciences et technologies du numérique Accéder directement au contenu
Article Dans Une Revue Graphs and Combinatorics Année : 2013

Neighbor Sum Distinguishing Index

Résumé

We consider proper edge colorings of a graph G using colors of the set {1, . . . , k}. Such a coloring is called neighbor sum distinguishing if for any pair of adjacent vertices x and y the sum of colors taken on the edges incident to x is different from the sum of colors taken on the edges incident to y. The smallest value of k in such a coloring of G is denoted by ndiΣ(G). In the paper we conjecture that for any connected graph G ≠ C 5 of order n ≥ 3 we have ndiΣ(G) ≤ Δ(G) + 2. We prove this conjecture for several classes of graphs. We also show that ndiΣ(G) ≤ 7Δ(G)/2 for any graph G with Δ(G) ≥ 2 and ndiΣ(G) ≤ 8 if G is cubic.

Dates et versions

hal-01753341 , version 1 (29-03-2018)

Identifiants

Citer

Evelyne Flandrin, Antoni Marczyk, Jakub Przybylo, Jean-François Saclé, Mariusz Woźniak. Neighbor Sum Distinguishing Index. Graphs and Combinatorics, 2013, 29 (5), pp.1329-1336. ⟨10.1007/s00373-012-1191-x⟩. ⟨hal-01753341⟩
187 Consultations
0 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More