(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 $\mathrm{\Delta }\ge 12$ and $d=2$, the (2,1)-total labelling number ${\lambda }_2^T(G)$ is at most $\mathrm{\Delta }+2$.