Abstract
A new proof that the number of spanning trees of K m,n is m n−1 n m−1 is presented. The proof is similar to Prüfer’s proof of Cayley’s formula for the number of spanning trees of K n .
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References
R. Onadera, On the number of trees in a complete n-partite graph.Matrix Tensor Quart.23 (1972/73), 142–146.
H. Prüfer, Neuer Beweiss einer Satzes über Permutationen. Math. Phys. 27 (1918), 742–744.
H. I. Scoins, The number of trees with nodes of alternate parity. Proc. Cambridge Philos. Soc. 58 (1963), 12–16.
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© 1990 Physica-Verlag Heidelberg
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Hartsfield, N., Werth, J.S. (1990). Spanning Trees of the Complete Bipartite Graph. In: Bodendiek, R., Henn, R. (eds) Topics in Combinatorics and Graph Theory. Physica-Verlag HD. https://doi.org/10.1007/978-3-642-46908-4_38
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DOI: https://doi.org/10.1007/978-3-642-46908-4_38
Publisher Name: Physica-Verlag HD
Print ISBN: 978-3-642-46910-7
Online ISBN: 978-3-642-46908-4
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