A carregar...
Publicação
An introduction to Graphs on Groups
| Nome: | Descrição: | Tamanho: | Formato: | |
|---|---|---|---|---|
| 497.29 KB | Adobe PDF |
Autores
Orientador(es)
Resumo(s)
The present dissertation, titled An Introduction to Graphs on Groups, aims to study connections
between two fundamental areas of mathematics: groups and graphs.
In the first chapter we introduce the basic definitions and results that will be needed throughout this
essay. It has four sections. The first one is dedicated to Graph Theory, and it is mainly composed by basic
definitions and examples. The rest of the chapter focuses on Group Theory. In this part of the essay, we
introduce the different classes of groups with which we will be working on.
Chapter 2 is divided into four sections, one for each graph on group we will be working on: the commuting graph, the power graph, the enhanced power graph and the non-generating graph. Here
we study for which groups each of these graphs is complete or null, we deduce some results regarding
maximal cliques and present a few results regarding diameter and connectivity. Several examples are
given.
The next chapter has as objective to study some differences (in the sense of subtraction) between the
graphs presented in Chapter 2. Hence, we begin Chapter 3 with the definition of graph hierarchy and
we show that it is well defined. Next, we study when two graphs in said hierarchy are equal. We then
compute the difference between pairs of graphs in the hierarchy. In particular, we study the difference
between the enhanced power graph and the power graph and the difference between the non-generating
graph and the commuting graph. For each of these new classes of graphs, we determine their isolated
vertices, study connectivity, diameter, and give several examples.
We finish the main body of this dissertation with Chapter 4. Here we define and study two
differences of graphs that have not yet, to the best of our knowledge, been considered.
Descrição
Tese de Mestrado, Matemática, 2024, Universidade de Lisboa, Faculdade de Ciências
Palavras-chave
Grafos em grupos Hierarquia de grafos Diferença na hierarquia Conectividade Diâmetro Teses de mestrado - 2024