Graphs and Combinatorics

, Volume 29, Issue 5, pp 1329–1336

Neighbor Sum Distinguishing Index

Authors

  • Evelyne Flandrin
    • L R I, UMR 8623, Bât. 490Université de Paris-Sud
    • AGH University of Science and Technology
  • Jakub Przybyło
    • AGH University of Science and Technology
  • Jean-François Saclé
    • L R I, UMR 8623, Bât. 490Université de Paris-Sud
  • Mariusz Woźniak
    • AGH University of Science and Technology
Open AccessOriginal Paper

DOI: 10.1007/s00373-012-1191-x

Cite this article as:
Flandrin, E., Marczyk, A., Przybyło, J. et al. Graphs and Combinatorics (2013) 29: 1329. doi:10.1007/s00373-012-1191-x

Abstract

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.

Keywords

Proper edge coloring Neighbor-distinguishing index Neighbor sum distinguishing coloring Chromatic index

Mathematics Subject Classification

05C15

Copyright information

© The Author(s) 2012