Neighbor sum distinguishing index of 2-degenerate graphs |
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Authors: | Xiaolan Hu Yaojun Chen Rong Luo Zhengke Miao |
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Affiliation: | 1.School of Mathematics and Statistics,Central China Normal University,Wuhan,China;2.Department of Mathematics,Nanjing University,Nanjing,China;3.School of Mathematics and Statistics,Jiangsu Normal University,Xuzhou,China |
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Abstract: | We consider proper edge colorings of a graph G using colors in \(\{1,\ldots ,k\}\). Such a coloring is called neighbor sum distinguishing if for each pair of adjacent vertices u and v, the sum of the colors of the edges incident with u is different from the sum of the colors of the edges incident with v. The smallest value of k in such a coloring of G is denoted by \({\mathrm ndi}_{\Sigma }(G)\). In this paper we show that if G is a 2-degenerate graph without isolated edges, then \({\mathrm ndi}_{\Sigma }(G)\le \max \{\Delta (G)+2,7\}\). |
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