Nonplanarity of Iterated Line Graphs. (24th December 2020)

• Record Type: Journal Article
• Authors: Wang, Jing
• Other Names: Peris Alfred Academic Editor.
• Is Part Of: Journal of mathematics. Volume 2020(2020)
• Publication Date: 2020-12-24
• Subjects: Mathematics -- Periodicals; Mathematics; Periodicals; 510
• DOI: 10.1155/2020/5752806
• Languages: English
• ISSNs: 2314-4629

Abstract

Abstract : The 1-crossing index of a graph G is the smallest integer k such that the k th 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.