On Neighbor-Distinguishing Index of Planar Graphs


  • Contract grant sponsor: APVV; contract grant number: APVV-0023-10 (M.H.); contract grant sponsor: VEGA; contract grant number: 1/0652/12 (M.H.); contract grant sponsor: NSFC; contract grant number: 11101377 (D.H.), 11301486 (D.H.), 11071223 (W.W.); contract grant sponsor: ZJNSFC; contract grant number: LQ13A010009 (D.H.), Z6090150 (W.W.).


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 math formula 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.