Nonplanarity of Iterated Line Graphs
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 r...
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| Format: | Article |
| Language: | English |
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Wiley
2020-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2020/5752806 |
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| _version_ | 1832551665209704448 |
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| author | Jing Wang |
| author_facet | Jing Wang |
| author_sort | Jing Wang |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-47653b06cc48422babd0c93c9e3bce4f |
| institution | Kabale University |
| issn | 2314-4629 2314-4785 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-47653b06cc48422babd0c93c9e3bce4f2025-02-03T06:00:49ZengWileyJournal of Mathematics2314-46292314-47852020-01-01202010.1155/2020/57528065752806Nonplanarity of Iterated Line GraphsJing Wang0Department of Mathematics and Computer Science, Changsha University, Changsha 410003, ChinaThe 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.http://dx.doi.org/10.1155/2020/5752806 |
| spellingShingle | Jing Wang Nonplanarity of Iterated Line Graphs Journal of Mathematics |
| title | Nonplanarity of Iterated Line Graphs |
| title_full | Nonplanarity of Iterated Line Graphs |
| title_fullStr | Nonplanarity of Iterated Line Graphs |
| title_full_unstemmed | Nonplanarity of Iterated Line Graphs |
| title_short | Nonplanarity of Iterated Line Graphs |
| title_sort | nonplanarity of iterated line graphs |
| url | http://dx.doi.org/10.1155/2020/5752806 |
| work_keys_str_mv | AT jingwang nonplanarityofiteratedlinegraphs |