(2,1)-Total labeling of planar graphs with large maximum degree
  The ($d$,1)-total labelling of graphs was introduced by Havet and Yu. In this paper, we prove that, for planar graph $G$ with maximum degree $\Delta\geq12$ and $d=2$, the (2,1)-total labelling number $\lambda_2^T(G)$ is at most $\Delta+2$. 
Yong Yu, Xin Zhang, Guanghui Wang, Jinbo Li
math.CO cs.DM