2-dipath and oriented L(2, 1)-labelings of some families of oriented planar graphs

In this paper, we improve the existing bounds [Calamoneri, T. and B. Sinaimeri, L ( 2 , 1 ) -Labeling of Oriented Planar Graphs (Extended Abstract), in: Proc. 12th Italian Conference on Theoretical Computer Science, (2010)] for 2-dipath and oriented L ( 2 , 1 ) span for the class of planar graphs with girth 5, 11, 16, cactus, wheels and leaf independent Halin graphs. Some of these bounds are tight.