A new simple proof of cayles’s formula and its relationship with the Kirkwood – Salzburg equations

  • O. L. Rebenko Institute of Mathematics, National Academy of Sciences of Ukraine, Kyiv
Keywords: forests, trees, Cayley's formula

Abstract

UDC 519.1

A new very simple proof of the formula for the number of labeled root forest-graphs with a given number of vertices is proposed. As a partial case of this formula, we obtain Cayley's formula.

References

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J. W. Moon, Various proofs of Cayley's formula for counting trees, A Seminar on Graph Theory (Ed. F.~Harary), Holt, Rinehart, and Winston, New York (1967), p.~70 – 78.

O. L. Rebenko, On the connection of some approaches to solving the Kirkwood – Salzburg equations, Ukr. Math. J., 73, № 3, 93 – 106 (2021).

Lajos Takacs, On Cayley’s formula for counting forests, J. Combin. Theory, Ser. A, 53, 321 – 323 (1990).

Published
27.11.2022
How to Cite
RebenkoO. L. “A New Simple Proof of cayles’s Formula and Its Relationship With the Kirkwood – Salzburg Equations”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 74, no. 10, Nov. 2022, pp. 1441 -44, doi:10.37863/umzh.v74i10.7156.
Section
Short communications