Editing Graph isomorphism (section)

== Whitney theorem ==
{{main article|Whitney graph isomorphism theorem}}
[[File:Whitneys theorem exception.svg|right|thumb|200px|The exception to Whitney's theorem: these two graphs are not isomorphic but have isomorphic line graphs.]]
The '''Whitney graph isomorphism theorem''',<ref>{{cite journal|last=Whitney|first=Hassler|title=Congruent Graphs and the Connectivity of Graphs|journal=American Journal of Mathematics|date=January 1932|volume=54|issue=1|pages=150–168|jstor=2371086|doi=10.2307/2371086|hdl=10338.dmlcz/101067|hdl-access=free}}</ref> shown by [[Hassler Whitney]], states that two connected graphs are isomorphic if and only if their [[line graph]]s are isomorphic, with a single exception: ''K''<sub>3</sub>, the [[complete graph]] on three vertices, and the [[complete bipartite graph]] ''K''<sub>1,3</sub>, which are not isomorphic but both have ''K''<sub>3</sub> as their line graph. The Whitney graph theorem can be extended to [[hypergraph]]s.<ref>Dirk L. Vertigan, Geoffrey P. Whittle: A 2-Isomorphism Theorem for Hypergraphs. J. Comb. Theory, Ser. B 71(2): 215–230. 1997.</ref>