On (p, 1)-Total Labelling of Some 1-Planar Graphs

Discussiones Mathematicae Graph Theory

Niu Bei¹  Zhang Xin¹ 

[1] School of Mathematics and Statistics, Xidian University, Xi’an, 710071, China;

关键词: 1-planar graph;    total coloring;    (p,1)-total labelling;    structural theorem;    05c15;    05c10;   

DOI  :  10.7151/dmgt.2208

来源: DOAJ

【 摘 要 】

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 (p ≥ 2) of every 1-planar graph G is at most Δ(G) + 2p − 2 provided that Δ (G) ≥ 6p + 7 or Δ (G) ≥ 4p + 6 and G is triangle-free.

【 授权许可】

Unknown