Whitney's theorem

proper noun

A theorem stating that two connected graphs are isomorphic if and only if their line graphs are isomorphic, with a single exception: K₃, the complete graph on three vertices, and the complete bipartite graph K_(1,3), which are not isomorphic but both have K₃ as their line graph.

“Whitney's theorem can be extended to hypergraphs.”

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Meanings

proper noun
  1. A theorem stating that two connected graphs are isomorphic if and only if their line graphs are isomorphic, with a single exception: K₃, the complete graph on three vertices, and the complete bipartite graph K_(1,3), which are not isomorphic but both have K₃ as their line graph.

    Whitney's theorem can be extended to hypergraphs.

Origin

Introduced by Hassler Whitney (1907–1989), American mathematician.

Full word history & related roots →
Cite this entry
APA

Whitney's theorem. (n.d.). In WatkinsX Dictionary. Retrieved November 4, 2026, from https://dictionary.watkinsx.com/word/Whitney's%20theorem

MLA

“Whitney's theorem.” WatkinsX Dictionary, https://dictionary.watkinsx.com/word/Whitney's%20theorem. Accessed November 4, 2026.

Chicago

WatkinsX Dictionary, s.v. “Whitney's theorem,” accessed November 4, 2026, https://dictionary.watkinsx.com/word/Whitney's%20theorem.

Source: Whitney's theorem on Wiktionary, CC BY-SA 4.0.