The 1-crossing index of a graph is the smallest integer such that the th iterated line graph of has crossing number greater than 1. In this paper, we show that the 1-crossing index of a graph is either infinite or it is at most 5. Moreover, we give a full characterization of all graphs with respect to their 1-crossing index.

中文翻译：

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折线图的非平面性

图的1-crossing索引是最小的整数，因此它的迭代线图的交叉数大于1。在本文中，我们显示了图的1-crossing索引是无限的或最大。 5.此外，我们对所有图形的1交叉索引进行了全面表征。