Alianças defensivas em grafos
Autor(a) principal: | |
---|---|
Data de Publicação: | 2010 |
Tipo de documento: | Dissertação |
Idioma: | por |
Título da fonte: | Repositório Institucional da UFG |
Texto Completo: | http://repositorio.bc.ufg.br/tede/handle/tde/3008 |
Resumo: | A defensive alliance in graph G = (V;E) is a set of vertices S V satisfying the condition that every vertex v 2 S has at most one more neighbor in V S than S. Due to this type of alliance, the vertices in S together defend themselves to the vertices in V S. This dissertation introduces the basic concepts for the understanding of alliances in graphs, along with a variety of alliances and their numbers and provides some mathematical properties for these alliances, focusing mainly on defensive alliances in graphs. It shows theorems, corollaries, lemmas, propositions and observations with appropriate proofs with respect to the minimum degree of a graph G d(G), the maximum degree D(G), the algebraic connectivity μ, the total dominanting set gt(G), the eccentricity, the edge connectivity l(G), the chromatic number c(G), the (vertex) independence number b0(G), the vertex connectivity k(G), the order of the largest clique w(G) and the domination number g(G). It also shows a generalization of defensive alliances, called defensive kalliance, and the definition and properties of a security set in G. A secure set S V of graph G = (V;E) is a set whose every nonempty subset can be successfully defended of an attack, under appropriate definitions of “attack” and “defence”. |
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Barbosa, Rommel Melgaçohttp://buscatextual.cnpq.br/buscatextual/visualizacv.do?id=K4786013D6Martins, Wellington Santoshttp://buscatextual.cnpq.br/buscatextual/visualizacv.do?id=K4782112U1Tronto, Íris Fabiana de Barceloshttp://buscatextual.cnpq.br/buscatextual/visualizacv.do?id=K4707515J4http://buscatextual.cnpq.br/buscatextual/visualizacv.do?id=K4232736P3Dias, Elisângela Silva2014-09-04T17:02:47Z2010-03-26DIAS, Elisângela Silva. Alianças defensivas em grafos. 2010. 105 f. Dissertação (Mestrado em Ciências da Computações) - Universidade Federal de Goiás, Goiâniahttp://repositorio.bc.ufg.br/tede/handle/tde/3008ark:/38995/0013000009k6pA defensive alliance in graph G = (V;E) is a set of vertices S V satisfying the condition that every vertex v 2 S has at most one more neighbor in V S than S. Due to this type of alliance, the vertices in S together defend themselves to the vertices in V S. This dissertation introduces the basic concepts for the understanding of alliances in graphs, along with a variety of alliances and their numbers and provides some mathematical properties for these alliances, focusing mainly on defensive alliances in graphs. It shows theorems, corollaries, lemmas, propositions and observations with appropriate proofs with respect to the minimum degree of a graph G d(G), the maximum degree D(G), the algebraic connectivity μ, the total dominanting set gt(G), the eccentricity, the edge connectivity l(G), the chromatic number c(G), the (vertex) independence number b0(G), the vertex connectivity k(G), the order of the largest clique w(G) and the domination number g(G). It also shows a generalization of defensive alliances, called defensive kalliance, and the definition and properties of a security set in G. A secure set S V of graph G = (V;E) is a set whose every nonempty subset can be successfully defended of an attack, under appropriate definitions of “attack” and “defence”.Uma aliança defensiva no grafo G = (V;E) é um conjunto de vértices S V satisfazendo a condição de que todo vértice v 2 S tem no máximo um vizinho a mais em V S que em S. Devido a este tipo de aliança, os vértices em S juntam para se defenderem dos vértices em V S. Nesta dissertação, são introduzidos os conceitos básicos para o entendimentos das alianças em grafos, junto com uma variedade de tipos de alianças e seus respectivos números, bem como são fornecidas algumas propriedades matemáticas para estas alianças, focando principalmente nas alianças defensivas em grafos. Apresentamos teoremas, corolários, lemas, proposições e observações com as devidas provas com relação ao grau mínimo de um grafo G d(G), ao grau máximo D(G), à conectividade algébrica μ, ao conjunto dominante total gt(G), à excentricidade, à conectividade de arestas l(G), ao número cromático c(G), ao número de independência (de vértices) b0(G), à conectividade de vértices k(G), à ordem da maior clique w(G) e ao número de dominação g(G). Também é mostrada a generalização de alianças defensivas, chamada k-aliança defensiva, e a definição e propriedades de um conjunto seguro em G. Um conjunto seguro S V do grafo G = (V;E) é um conjunto no qual todo subconjunto não-vazio pode ser defendido com sucesso de um ataque, sob as definições apropriadas de “ataque” e “defesa”.Submitted by Jaqueline Silva (jtas29@gmail.com) on 2014-09-04T17:02:47Z No. of bitstreams: 2 Dissertacao Elisangela Silva Dias.pdf: 846122 bytes, checksum: 357f425f14050b1601ed04cbcd4d9165 (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5)Made available in DSpace on 2014-09-04T17:02:47Z (GMT). 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dc.title.por.fl_str_mv |
Alianças defensivas em grafos |
title |
Alianças defensivas em grafos |
spellingShingle |
Alianças defensivas em grafos Dias, Elisângela Silva Alianças em grafos Alianças defensivas Conjuntos seguros Alliances in graphs Defensive alliances Secure sets CIENCIA DA COMPUTACAO::SISTEMAS DE COMPUTACAO CIENCIA DA COMPUTACAO::TEORIA DA COMPUTACAO |
title_short |
Alianças defensivas em grafos |
title_full |
Alianças defensivas em grafos |
title_fullStr |
Alianças defensivas em grafos |
title_full_unstemmed |
Alianças defensivas em grafos |
title_sort |
Alianças defensivas em grafos |
author |
Dias, Elisângela Silva |
author_facet |
Dias, Elisângela Silva |
author_role |
author |
dc.contributor.advisor1.fl_str_mv |
Barbosa, Rommel Melgaço |
dc.contributor.advisor1Lattes.fl_str_mv |
http://buscatextual.cnpq.br/buscatextual/visualizacv.do?id=K4786013D6 |
dc.contributor.referee1.fl_str_mv |
Martins, Wellington Santos |
dc.contributor.referee1Lattes.fl_str_mv |
http://buscatextual.cnpq.br/buscatextual/visualizacv.do?id=K4782112U1 |
dc.contributor.referee2.fl_str_mv |
Tronto, Íris Fabiana de Barcelos |
dc.contributor.referee2Lattes.fl_str_mv |
http://buscatextual.cnpq.br/buscatextual/visualizacv.do?id=K4707515J4 |
dc.contributor.authorLattes.fl_str_mv |
http://buscatextual.cnpq.br/buscatextual/visualizacv.do?id=K4232736P3 |
dc.contributor.author.fl_str_mv |
Dias, Elisângela Silva |
contributor_str_mv |
Barbosa, Rommel Melgaço Martins, Wellington Santos Tronto, Íris Fabiana de Barcelos |
dc.subject.por.fl_str_mv |
Alianças em grafos Alianças defensivas Conjuntos seguros |
topic |
Alianças em grafos Alianças defensivas Conjuntos seguros Alliances in graphs Defensive alliances Secure sets CIENCIA DA COMPUTACAO::SISTEMAS DE COMPUTACAO CIENCIA DA COMPUTACAO::TEORIA DA COMPUTACAO |
dc.subject.eng.fl_str_mv |
Alliances in graphs Defensive alliances Secure sets |
dc.subject.cnpq.fl_str_mv |
CIENCIA DA COMPUTACAO::SISTEMAS DE COMPUTACAO CIENCIA DA COMPUTACAO::TEORIA DA COMPUTACAO |
description |
A defensive alliance in graph G = (V;E) is a set of vertices S V satisfying the condition that every vertex v 2 S has at most one more neighbor in V S than S. Due to this type of alliance, the vertices in S together defend themselves to the vertices in V S. This dissertation introduces the basic concepts for the understanding of alliances in graphs, along with a variety of alliances and their numbers and provides some mathematical properties for these alliances, focusing mainly on defensive alliances in graphs. It shows theorems, corollaries, lemmas, propositions and observations with appropriate proofs with respect to the minimum degree of a graph G d(G), the maximum degree D(G), the algebraic connectivity μ, the total dominanting set gt(G), the eccentricity, the edge connectivity l(G), the chromatic number c(G), the (vertex) independence number b0(G), the vertex connectivity k(G), the order of the largest clique w(G) and the domination number g(G). It also shows a generalization of defensive alliances, called defensive kalliance, and the definition and properties of a security set in G. A secure set S V of graph G = (V;E) is a set whose every nonempty subset can be successfully defended of an attack, under appropriate definitions of “attack” and “defence”. |
publishDate |
2010 |
dc.date.issued.fl_str_mv |
2010-03-26 |
dc.date.accessioned.fl_str_mv |
2014-09-04T17:02:47Z |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/masterThesis |
format |
masterThesis |
status_str |
publishedVersion |
dc.identifier.citation.fl_str_mv |
DIAS, Elisângela Silva. Alianças defensivas em grafos. 2010. 105 f. Dissertação (Mestrado em Ciências da Computações) - Universidade Federal de Goiás, Goiânia |
dc.identifier.uri.fl_str_mv |
http://repositorio.bc.ufg.br/tede/handle/tde/3008 |
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ark:/38995/0013000009k6p |
identifier_str_mv |
DIAS, Elisângela Silva. Alianças defensivas em grafos. 2010. 105 f. Dissertação (Mestrado em Ciências da Computações) - Universidade Federal de Goiás, Goiânia ark:/38995/0013000009k6p |
url |
http://repositorio.bc.ufg.br/tede/handle/tde/3008 |
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por |
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por |
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600 600 600 600 |
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http://creativecommons.org/licenses/by-nc-nd/4.0/ |
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openAccess |
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Universidade Federal de Goiás |
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Programa de Pós-graduação em Ciência da Computação (INF) |
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UFG |
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Brasil |
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Instituto de Informática - INF (RG) |
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Universidade Federal de Goiás |
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