JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2023, Vol. 58 ›› Issue (12): 134-139.doi: 10.6040/j.issn.1671-9352.0.2022.276

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Adjacent vertex distinguishing edge coloring of IC-planar graphs without intersecting triangles

Jin LI(),Changqing XU*()   

  1. School of Science, Hebei University of Technology, Tianjin 300401, China
  • Received:2022-05-02 Online:2023-12-20 Published:2023-12-19
  • Contact: Changqing XU E-mail:lj13663389266@163.com;chqxu@hebut.edu.cn

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Abstract:

Let φ be an l-proper edge coloring of graph G and Cφ(u) be the color set of all edges incident with vertex u of G. An l-adjacent vertex distinguishing edge coloring of a graph G is the coloring φ such that Cφ(u) and Cφ(v) are distinct for any edge uv of G, denoted by an l-avd coloring. The minimum positive integer l for an l-avd coloring of G is the adjacent vertex distinguishing edge chromatic number, denoted by χ′a(G). In this paper, we study the adjacent vertex distinguishing edge coloring of an IC-normal planar graph G without intersecting triangles by using the discharging method and get that χ′a(G)≤max{Δ(G)+2, 12}.

Key words: adjacent vertex distinguishing edge coloring, discharging method, IC-normal planar graph

CLC Number: 

  • O157.5

Table 1

Relation between dG(u) and dT(u)"

条件 dT(u)
3≤dG(u)≤6 dT(u)=dG(u)
dG(u)=7 dT(u)≥6
dG(u)=8 dT(u)≥6
dG(u)=9 dT(u)≥7
dG(u)≥10 dT(u)≥6
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[1] LIU Zhuo-ya, XU Chang-qing. Adjacent vertex distinguishing edge coloring of planar graphs without intersecting triangles [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2020, 55(9): 36-41.
[2] SUN Lin, CAI Hua. On the vertex-arboricity of embedded graphs [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2015, 50(02): 38-42.
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