Counting of spanning trees of a complete graph
DOI:
https://doi.org/10.5902/2179460X27277Keywords:
Trees, Spanning Trees, Cayley’s Formula, Complete Graphs, Inverse Process of Cayley-PruferAbstract
In 1889, Arthur Cayley published an article that contained a formula for counting the spanning trees of a complete graph. This theorem says that: Let n E N and Kn the complete graph with n vertices. Then the number of spanning trees of Kn is established by n n-2: The present work is constituted by a brief literary review about the basic concepts and results of the graph theory and detailed demonstration of the Cayley’s Formula, given by the meticulous construction of a bijection between the set of the spanning trees and a special set of numeric sequences. At the end we bring an algorithm that describes a precise construction of the spanning trees obtained of Kn from Cayley-Prufer sequences.
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References
Abu-Sbeih, M. Z. (1990). On the number of spanning trees of Kn and Km;n. Discrete Mathematics, North-Holland, 84, 205–207.
Bondy, J. A., Murty, U. R. S. (1982). Graph theory with applications, 5o edn. New York: North Holland.
Domingues, H. H., Iezzi, G. (2003). Algebra Moderna ´ , 4o edn. Sao Paulo: Atual.
Fracasso, P. (2008). Analise de t ´ ecnicas para amostragem e sele ´ c¸ao de v ˜ ertices no planejamento probabil ´ ´ıstico de mapa de rotas. Dissertac¸ao de mestrado, Escola polit ˜ ecnica da USP. ´
Harary, F. (1969). Graph Theory, 1o edn. Menlo Park: Addison Wesley Pub. Co. Inc..
Junior, E. R. H., Nicoletti, M. C. (2006). ´ Fundamentos da teoria dos grafos para computac¸ao ˜ , 1o edn. Sao Carlos: Edufscar. ˜
Konzen, D. C. (1997). Automata and computability, 1o edn. Springer New York.
Orsini, L. Q., Consonni, D. (2002). Curso de circuitos eletricos ´ , 2o edn. Edgard Blucher Ltda. ¨
Wilson, R. J. (1996). Introduction to graph theory, 4o edn. London: Prentice-Hall.
Wu, B. Y., Chao, K. (2004). Spanning trees and optimization problems, 1o edn. Chapman & Hall/CRC Press, USA.
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