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...

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Detalles Bibliográficos
Autores: Porto, Anderson Luiz Pedrosa, Bessa, Vagner Rodrigues de, Aguiar, Mattheus Pereira da Silva, Vieira, Mariana Martins
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
Descripción
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.