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Wang, W.F. and Wang, Y.Q. (2015) Some Bounds on the Neighbor-Distinguishing Index of Graphs. Discrete Mathematics, 338, 2006-2013.
https://doi.org/10.1016/j.disc.2015.05.007

has been cited by the following article:

• TITLE: Neighbor Sum Distinguishing Index of Graphs with Maximum Average Degree

  AUTHORS: Xizhao Sun

  KEYWORDS: Proper Edge Coloring, Neighbor Sum Distinguishing Edge Coloring, Maximum Average Degree, Combinatorial Nullstellensatz

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.9 No.10, October 27, 2021

  ABSTRACT: A proper k-edge coloring of a graph G = (V(G), E(G)) is an assignment c: E(G) → {1, 2, …, k} such that no two adjacent edges receive the same color. A neighbor sum distinguishing k-edge coloring of G is a proper k-edge coloring of G such that for each edge uv ∈ E(G). The neighbor sum distinguishing index of a graph G is the least integer k such that G has such a coloring, denoted by χ’Σ(G). Let be the maximum average degree of G. In this paper, we prove χ’Σ(G) ≤ max{9, Δ(G) +1} for any normal graph G with . Our approach is based on the discharging method and Combinatorial Nullstellensatz.