On (p,1)-total labelling of some 1-planar graphs
Bei Niu, Xin Zhang · Discussiones Mathematicae Graph Theory · 2019
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 (G) + 2p -2 provided that (G) 6p + 7 or (G) 4p + 6 and G is triangle-free.