Geodesic
L(2, 1)-Labelings of Some Families of Oriented Planar Graphs
Discussiones Mathematicae. Graph Theory, Tome 34 (2014) no. 1, pp. 31-48.

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In this paper we determine, or give lower and upper bounds on, the 2-dipath and oriented L(2, 1)-span of the family of planar graphs, planar graphs with girth 5, 11, 16, partial k-trees, outerplanar graphs and cacti.
Keywords: homomorphism, planar graph, girth, partial k-tree, outerplanar graph, cactus, 2-dipath L(2, 1)-labeling, oriented L(2, 1)-labeling 
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Sen, Sagnik. L(2, 1)-Labelings of Some Families of Oriented Planar Graphs. Discussiones Mathematicae. Graph Theory, Tome 34 (2014) no. 1, pp. 31-48. http://geodesic.mathdoc.fr/item/DMGT_2014_34_1_a2/

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