Cografos integrais

Detalhes bibliográficos
Ano de defesa: 2021
Autor(a) principal: Ghisleni, Luiza de Paula
Orientador(a): Não Informado pela instituição
Banca de defesa: Não Informado pela instituição
Tipo de documento: Dissertação
Tipo de acesso: Acesso aberto
Idioma: por
Instituição de defesa: Universidade Federal de Santa Maria
Brasil
Matemática
UFSM
Programa de Pós-Graduação em Matemática
Centro de Ciências Naturais e Exatas
Programa de Pós-Graduação: Não Informado pela instituição
Departamento: Não Informado pela instituição
País: Não Informado pela instituição
Palavras-chave em Português:
Link de acesso: http://repositorio.ufsm.br/handle/1/23232
Resumo: The search for integral cographs is a topic of interest in Spectral Graph Theory. From this, and motivated by the structural characteristics of these graphs, and by their spectral properties, we propose, in this dissertation, to show that two distinct techniques (algorithmic and combinatorial) can be effectively used to characterize, or determine classes of integral cographs. Through balanced cotrees, we started from cographs associated with balanced cotrees, and with the aid of Algorithm Diagonalize( , ) we determine the eigenvalues of the respective cograph, which are integers; and through combinatorial triangles, we determine which cographs are integrals, of the associates with the triangle Determinant Hosoya Triangle ℋ. The main results obtained are the Theorem 3.4.4, from the article by Allem and Tura (2020), the Theorem 4.3.8 and the Proposition 4.3.6, from the article by Ching, Flórez and Mukhrjee (2020). These lead us to characterize that for = 3 and = 3 + 1, the cographs, respectively, with and without loops, associated to the adjacency matrices * 2 and 2, are integrals; and cographs with balanced cotrees , also they are integrals.