O método bijetivo e a fórmula de Cayley sobre árvores

• Autor(a) principal: Castro, Francisco Alberto Cavalcante de
• Data de Publicação: 2018
• Tipo de documento: Dissertação
• Idioma: por
• Título da fonte: Repositório Institucional da Universidade Federal do Ceará (UFC)
• Texto Completo: http://www.repositorio.ufc.br/handle/riufc/36872
• topic: Teorema de Cayley; Árvores (Teoria dos grafos); Princípio bijetivo; Cayley's Theorem; Trees (Graph theory); Bijective principle

The objective of this work is to present the Bijective Principle as a counting method and to use it to demonstrate Cayley's formula about the number of trees labeled with a given set of vertices. This is an interesting method of counting which consists in observing that the existence of a bijection between two finite sets implies that such sets have the same amount of elements. To understand it better, we will briefly review functions and then introduce several applications. And to understand Cayley's formula we need to introduce some introductory concepts on Graph Theory. Proof of this formula is made using the so-called Prüfer Code, which will also be presented here.