Abstract
A proper k-edge coloring of a graph G is an assignment of one of k colors to each edge of G such that there are no two edges with the same color incident to a common vertex. Let f (v)denote the sum of colors of the edges incident to v. A k-neighbor sum distinguishing edge coloring of G is a proper k-edge coloring of G such that for each edge uv ∈ E(G), f (u) ≠ f (v). By \({\chi^\prime_{\sum} }(G)\), we denote the smallest value k in such a coloring of G. Letmad(G) denote the maximum average degree of a graph G. In this paper, we prove that every normal graph with mad \((G) < \tfrac{{10}}{3}\) and Δ(G) ≥ 8 admits a(Δ(G) + 2)-neighbor sum distinguishing edge coloring. Our approach is based on the Combinatorial Nullstellensatz and discharging method.
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Supported by the Natural Science Foundation of Shandong Provence (Grant Nos. ZR2018BA010, ZR2016AM01) and the National Natural Science Foundation of China (Grant No. 11571258)
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Wang, J.H., Qiu, B.J. & Cai, J.S. Neighbor Sum Distinguishing Index of Sparse Graphs. Acta. Math. Sin.-English Ser. 36, 673–690 (2020). https://doi.org/10.1007/s10114-020-9027-8
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DOI: https://doi.org/10.1007/s10114-020-9027-8
Keywords
- Proper edge coloring
- neighbor sum distinguishing edge coloring
- maximum average degree
- Combinatorial Nullstellensatz