Neighbor sum distinguishing index of 2-degenerate graphs

Xiaolan Hu (), Yaojun Chen (), Rong Luo () and Zhengke Miao ()
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Xiaolan Hu: Central China Normal University
Yaojun Chen: Nanjing University
Rong Luo: Jiangsu Normal University
Zhengke Miao: Jiangsu Normal University

Journal of Combinatorial Optimization, 2017, vol. 34, issue 3, No 11, 798-809

Abstract: Abstract We consider proper edge colorings of a graph G using colors in $$\{1,\ldots ,k\}$$ { 1 , … , 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 $${\mathrm ndi}_{\Sigma }(G)$$ n d i Σ ( G ) . In this paper we show that if G is a 2-degenerate graph without isolated edges, then $${\mathrm ndi}_{\Sigma }(G)\le \max \{\Delta (G)+2,7\}$$ n d i Σ ( G ) ≤ max { Δ ( G ) + 2 , 7 } .

Keywords: Neighbor sum distinguishing edge colorings; 2-Degenerate; Maximum degree (search for similar items in EconPapers)
Date: 2017
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DOI: 10.1007/s10878-017-0110-8

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