O número envoltório P3 e o número envoltório geodético em produtos de grafos
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| Main Author: | |
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| Publication Date: | 2016 |
| Format: | Master thesis |
| Language: | por |
| Source: | Repositório Institucional da UFG |
| Download full: | http://repositorio.bc.ufg.br/tede/handle/tede/6583 |
Summary: | 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 |
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