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Two-Distance Vertex-Distinguishing Index of Sparse Subcubic Graphs

  • Loumngam Kamga Victor
  • Juan Liu
  • Weifan WangEmail author
Article
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Abstract

The 2-distance vertex-distinguishing index \(\chi '_\mathrm{d2}(G)\) of a graph G is the minimum number of colors required for a proper edge coloring of G such that any pair of vertices at distance two have distinct sets of colors. It was conjectured that every subcubic graph G has \(\chi '_{\mathrm{d2}}(G)\le 5\). In this paper, we confirm this conjecture for subcubic graphs with maximum average degree less than \(\frac{8}{3}\).

Keywords

Subcubic graph Maximum average degree Edge coloring 2-Distance vertex-distinguishing index AVD edge coloring 

Mathematics Subject Classification

05C15 

Notes

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Copyright information

© Malaysian Mathematical Sciences Society and Penerbit Universiti Sains Malaysia 2019

Authors and Affiliations

  1. 1.Department of MathematicsZhejiang Normal UniversityJinhuaChina

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