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.