Journal of Combinatorial Optimization

, Volume 36, Issue 1, pp 108–120 | Cite as

2-Distance vertex-distinguishing index of subcubic graphs

  • Victor Loumngam Kamga
  • Weifan Wang
  • Ying Wang
  • Min Chen


A 2-distance vertex-distinguishing edge coloring of a graph G is a proper edge coloring of G such that any pair of vertices at distance 2 have distinct sets of colors. The 2-distance vertex-distinguishing index \(\chi ^{\prime }_{\mathrm{d2}}(G)\) of G is the minimum number of colors needed for a 2-distance vertex-distinguishing edge coloring of G. Some network problems can be converted to the 2-distance vertex-distinguishing edge coloring of graphs. It is proved in this paper that if G is a subcubic graph, then \(\chi ^{\prime }_{\mathrm{d2}}(G)\le 6\). Since the Peterson graph P satisfies \(\chi ^{\prime }_{\mathrm{d2}}(P)=5\), our solution is within one color from optimal.


Subcubic graph Edge coloring 2-Distance vertex-distinguishing index Star-chromatic index 


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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  • Victor Loumngam Kamga
    • 1
  • Weifan Wang
    • 1
  • Ying Wang
    • 1
  • Min Chen
    • 1
  1. 1.Department of MathematicsZhejiang Normal UniversityJinhuaChina

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