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 \(\Delta (G)\ge 16\).

中文翻译：

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IC平面图的相邻顶点区分边缘着色

图G的相邻顶点区分边着色是每对相邻顶点被分配不同颜色集的固有边着色。G具有这种着色的最小颜色数由\(\chi '_a(G)\) 表示。由于张等人的一个重要猜想。(Appl Math Lett 15:623–626, 2002) 断言\(\chi '_a(G)\le \Delta (G)+2\)对于阶数至少为 6 的任何连通图G。通过应用放电方法，我们证明这个猜想对于任何具有\(\Delta (G)\ge 16\) 的IC 平面图G都是正确的。