A new simple proof of cayles’s formula and its relationship with the Kirkwood – Salzburg equations
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
M. Aigner, G. M. Ziegler, Proofs from the book, 4th ed., Springer-Verlag, Berlin (2010).
S. Guo, V. J. W. Guo, A recursive algorithm for trees and forests, Discrete Math., 340, 695 – 703 (2017).
R. A. Minlos, S. K. Poghosyan, Estimates of Ursell functions, group functions, and their derivatives, Theor. Math. Phys., 31, № 2, 408 – 418 (1977).
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).
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