Adjacent Vertex Distinguishing Edge Coloring of Planar Graphs Without 4-Cycles

  • Danjun HuangEmail author
  • Xiaoxiu Zhang
  • Weifan Wang
  • Ping Wang


The adjacent vertex distinguishing edge coloring of a graph G is a proper edge coloring of G such that the edge coloring set on any pair of adjacent vertices is distinct. The minimum number of colors required for an adjacent vertex distinguishing edge coloring of G is denoted by \(\chi _{a}'(G)\). It is observed that \(\chi _a'(G)\ge \Delta (G)+1\) when G contains two adjacent vertices of degree \(\Delta (G)\). In this paper, we prove that if G is a planar graph without 4-cycles, then \(\chi _a'(G)\le \max \{9,\Delta (G)+1\}\).


Adjacent vertex distinguishing edge coloring Planar graph Cycle 

Mathematics Subject Classification




This research was supported by Zhejiang Provincial Natural Science Foundation of China under Grant No. LY18A010014 (Danjun Huang), supported partially by NSFC under Grant No. 11771402 (Weifan Wang).


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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
  2. 2.Department of Mathematics, Statistics and Computer ScienceSt. Francis Xavier UniversityAntigonishCanada

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