Neighbor sum distinguishing colorings of graphs with maximum average degree less than $$\tfrac{{37}}
{{12}}$$ |
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Authors: | Bao Jian Qiu Ji Hui Wang Yan Liu |
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Institution: | School of Mathematical Sciences, University of Jinan, Jinan 250022, P. R. China |
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Abstract: | Let G be a graph and let its maximum degree and maximum average degree be denoted by Δ(G) and mad(G), respectively. A neighbor sum distinguishing k-edge colorings of graph G is a proper k-edge coloring of graph G such that, for any edge uv ∈ E(G), the sum of colors assigned on incident edges of u is different from the sum of colors assigned on incident edges of v. The smallest value of k in such a coloring of G is denoted by χ′∑(G). Flandrin et al. proposed the following conjecture that χ′∑ (G) ≤ Δ(G) + 2 for any connected graph with at least 3 vertices and G ≠ C5. In this paper, we prove that the conjecture holds for a normal graph with mad(G) < \(\tfrac{{37}}{{12}}\) and Δ(G) ≥ 7. |
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Keywords: | Neighbor sum distinguishing coloring combinatorial nullstellensatz maximum average degree proper colorings |
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