Geodesic
Adjacent vertex distinguishing edge-colorings of planar graphs with girth at least six
Discussiones Mathematicae. Graph Theory, Tome 31 (2011) no. 3, pp. 429-439

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An adjacent vertex distinguishing edge-coloring of a graph G is a proper edge-coloring o G such that any pair of adjacent vertices are incident to distinct sets of colors. The minimum number of colors required for an adjacent vertex distinguishing edge-coloring of G is denoted by χ'ₐ(G). We prove that χ'ₐ(G) is at most the maximum degree plus 2 if G is a planar graph without isolated edges whose girth is at least 6. This gives new evidence to a conjecture proposed in [Z. Zhang, L. Liu, and J. Wang, Adjacent strong edge coloring of graphs, Appl. Math. Lett., 15 (2002) 623-626.]
Keywords: edge-coloring, vertex-distinguishing, planar graph 
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Bu, Yuehua; Lih, Ko-Wei; Wang, Weifan. Adjacent vertex distinguishing edge-colorings of planar graphs with girth at least six. Discussiones Mathematicae. Graph Theory, Tome 31 (2011) no. 3, pp. 429-439. http://geodesic.mathdoc.fr/item/DMGT_2011_31_3_a1/