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Theorem: Number of Labeled Spanning Trees

In a complete graph K_n with n\ge 2 labeled vertices, the number of different spanning trees is n^{n-2}.

This theorem was discovered by Arthur Cayley (1821 - 1895).

Proofs: 1


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References

Bibliography

  1. Krumke S. O., Noltemeier H.: "Graphentheoretische Konzepte und Algorithmen", Teubner, 2005, 1st Edition