O número envoltório P3 e o número envoltório geodético em produtos de grafos

In this work, we consider the parameter hull number in two graph convexities, the P3- convexity and the geodetic convexity. In the P3-convexity, we present results on the P3- hull number on the Cartesian product, strong product and lexicographic product of graphs. In special, regarding to the Cartes...

Descripción completa

Detalles Bibliográficos
Autor: Nascimento, Julliano Rosa
Tipo de recurso: tesis de maestría
Estado:Versión publicada
Fecha de publicación:2016
País:Brasil
Institución:Universidade Federal de Goiás (UFG)
Repositorio:Repositório Institucional da UFG
Idioma:portugués
OAI Identifier:oai:repositorio.bc.ufg.br:tede/6583
Acceso en línea:http://repositorio.bc.ufg.br/tede/handle/tede/6583
Access Level:acceso abierto
Palabra clave:Convexidade P3
Convexidade geodética
Número envoltório
Produtos de grafos
Prismas complementares
P3-convexity
Geodetic convexity
Hull number
Graph products
Complementary prisms
CIENCIA DA COMPUTACAO::MATEMATICA DA COMPUTACAO
Descripción
Sumario:In this work, we consider the parameter hull number in two graph convexities, the P3- convexity and the geodetic convexity. In the P3-convexity, we present results on the P3- hull number on the Cartesian product, strong product and lexicographic product of graphs. In special, regarding to the Cartesian product, we proved a complexity result, in which we show, given a graph G resulting of a Cartesian product of two graphs and a positive integer k, is NP-complete to decide whether the P3-hull number of G is less than or equal k. We also consider the P3-hull number on complementary prisms GG of connected graphs G and G, in which we show a tighter upper bound than that found in the literature. In the geodetic convexity, we show results of the hull number on complementary prisms GG when G is a tree, when G is a disconnected graph and when G is a cograph. Finally, we also show that in the geodetic convexity, the hull number on the complementary prism GG is unlimited on connected graphs G and G, unlike what happens in the P3-convexity