On Line Graphs with Crossing Number 3

Mallikarjun Ghaleppa, Amit kumar Yadav and Amabelle Oliva Enanoria
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Mallikarjun Ghaleppa: Mathematics and Computing Unit, Preparatory Studies Center, University of Technology and Applied Sciences, Ibra, Oman.
Amit kumar Yadav: Mathematics and Computing Unit, Preparatory Studies Center, University of Technology and Applied Sciences, Ibra, Oman.
Amabelle Oliva Enanoria: Mathematics and Computing Unit, Preparatory Studies Center, University of Technology and Applied Sciences, Ibra, Oman.

International Journal of Research and Innovation in Social Science, 2025, vol. 9, issue 1, 2095-2102

Abstract: Kulli, Akka and Beineke obtained a characterization of planar graphs whose line graphs have crossing number 1. Akka, Jendrol, Klesvcv and Panshetty presented a characteri- zation of planar graphs whose line graphs have crossing number 2. The main result of this paper is a characterization of graphs whose line graphs have crossing number 3. The primary contribution of this paper is the characterization of graphs whose line graphs have a crossing number of three. Let be a graph and its line graph. The main result identifies necessary and sufficient structural properties of that ensure has a crossing number of three. Further research can expand on this work by examining families of graphs that exhibit higher crossing numbers and exploring computational approaches for practical applications in visualization and optimization.

Date: 2025
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