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Nonplanarity of Iterated Line Graphs

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  • Jing Wang
  • Alfred Peris

Abstract

The 1-crossing index of a graph G is the smallest integer k such that the kth iterated line graph of G 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.

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  • Jing Wang & Alfred Peris, 2020. "Nonplanarity of Iterated Line Graphs," Journal of Mathematics, Hindawi, vol. 2020, pages 1-8, December.
    • Handle: RePEc:hin:jjmath:5752806
    DOI: 10.1155/2020/5752806
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