On (p, 1)-total labelling of 1-planar graphs

  • Xin ZhangEmail author
  • Yong Yu
  • Guizhen Liu
Research Article


A graph is 1-planar if it can be drawn on the plane so that each edge is crossed by at most one other edge. In this paper, it is proved that the (p, 1)-total labelling number of every 1-planar graph G is at most Δ(G) + 2p − 2 provided that Δ(G) ≥ 8p+4 or Δ(G) ≥ 6p+2 and g(G) ≥ 4. As a consequence, the well-known (p, 1)-total labelling conjecture has been confirmed for some 1-planar graphs.


1-planar graph Alternating subgraph Master Total labelling Discharging 


05C10 05C15 


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Copyright information

© © Versita Warsaw and Springer-Verlag Wien 2011

Authors and Affiliations

  1. 1.School of MathematicsShandong UniversityJinanChina

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