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On Line Graphs with Crossing Number 1
Author(s) -
Kulli V. R.,
Akka D. G.,
Beineke L. W.
Publication year - 1979
Publication title -
journal of graph theory
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 54
eISSN - 1097-0118
pISSN - 0364-9024
DOI - 10.1002/jgt.3190030109
Subject(s) - crossing number (knot theory) , combinatorics , mathematics , line graph , graph , line (geometry) , 1 planar graph , discrete mathematics , geometry , intersection (aeronautics) , engineering , aerospace engineering
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.