The crossing number of a graph @math is the least number of crossings over all possible drawings of @math . We present a structural characterization of graphs with crossing number one.
Akka, Jendrol, Kle s c , and Panshetty @cite_15 obtained a characterization of planar graphs whose line graph has crossing number two.
@cite_15
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In this paper we deduce a necessary and sufficient condition for a line grah to have crossing number 1. In addition, we prove that the line graph of any nonplanar graph has crossing number greater than 2.