Adjacent vertex distinguishing edge coloring of IC-planar graphs

The adjacent vertex distinguishing edge coloring of a graph G is a proper edge coloring in which each pair of adjacent vertices is assigned different color sets. The smallest number of colors for which G has such a coloring is denoted by $$\chi '_a(G)$$ . An important conjecture due to Zhang et al. (Appl Math Lett 15:623–626, 2002) asserts that $$\chi '_a(G)\le \Delta (G)+2$$ for any connected graph G with order at least 6. By applying the discharging method, we show that this conjecture is true for any IC-planar graph G with $$\Delta (G)\ge 16$$ .