Counting of spanning trees of a complete graph
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...
| Autores: | , , , |
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2018 |
| País: | Brasil |
| Institución: | Universidade Federal de Santa Maria (UFSM) |
| Repositorio: | Revista Ciência e Natura (Online) |
| Idioma: | portugués |
| OAI Identifier: | oai:ojs.pkp.sfu.ca:article/27277 |
| Acceso en línea: | https://periodicos.ufsm.br/cienciaenatura/article/view/27277 |
| Access Level: | acceso abierto |
| Palabra clave: | Trees Spanning Trees Cayley’s Formula Complete Graphs Inverse Process of Cayley-Prufer |
| Sumario: | 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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