Neighbor-sum-distinguishing edge choosability of subcubic graphs

Jingjing Huo, Yiqiao Wang and Weifan Wang ()
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Jingjing Huo: Soochow University
Yiqiao Wang: Beijing University of Chinese Medicine
Weifan Wang: Zhejiang Normal University

Journal of Combinatorial Optimization, 2017, vol. 34, issue 3, No 7, 742-759

Abstract: Abstract A graph G is said to be neighbor-sum-distinguishing edge k-choose if, for every list L of colors such that L(e) is a set of k positive real numbers for every edge e, there exists a proper edge coloring which assigns to each edge a color from its list so that for each pair of adjacent vertices u and v the sum of colors taken on the edges incident to u is different from the sum of colors taken on the edges incident to v. Let $$\mathrm{ch}^{\prime }_{\sum ^p}(G)$$ ch ∑ p ′ ( G ) denote the smallest integer k such that G is neighbor-sum-distinguishing edge k-choose. In this paper, we prove that if G is a subcubic graph with the maximum average degree mad(G), then (1) $$\mathrm{ch}^{\prime }_{\sum ^p}(G)\le 7$$ ch ∑ p ′ ( G ) ≤ 7 ; (2) $$\mathrm{ch}^{\prime }_{\sum ^p}(G)\le 6$$ ch ∑ p ′ ( G ) ≤ 6 if $$\hbox {mad}(G)

Keywords: Subcubic graph; List neighbor-sum-distinguishing edge coloring; Maximum average degree; Combinatorial Nullstellensatz; 05C15 (search for similar items in EconPapers)
Date: 2017
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DOI: 10.1007/s10878-016-0104-y

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