English Dictionary

Whitney's theorem

固有名詞

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.

日本語の意味

連結グラフの線グラフが同型であるならば、元のグラフも同型であることを示す定理。ただし、例外として三角形グラフK₃と星型グラフK₁,₃は同型ではないが、どちらもK₃を線グラフとして持つ。

Whitney's theorem states that two connected graphs are isomorphic if and only if their line graphs are isomorphic, with the single exception that the complete graph on three vertices and the star K1,3 are not isomorphic despite both having K3 as their line graph.

ハスラー・ウィットニーの定理は、2つの連結グラフが辺のグラフ（ライン・グラフ）が同型であるときに限り元のグラフも同型であると述べており、唯一の例外として3頂点の完全グラフと星型の完全二部グラフK1,3は同型ではないにもかかわらず、どちらも辺のグラフがK3になることが挙げられます。

意味（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.