On Neighbor-Distinguishing Index of Planar Graphs
A proper edge coloring of a graph G without isolated edges is neighbor-distinguishing if any two adjacent vertices have distinct sets consisting of colors of their incident edges. The neighbor-distinguishing index of G is the minimum number ndi(G) of colors in a neighbor-distinguishing edge coloring of G. Zhang, Liu, and Wang in 2002 conjectured that if G is a connected graph of order at least 6. In this article, the conjecture is verified for planar graphs with maximum degree at least 12.
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