Alianças defensivas em grafos

• Autor(a) principal: Dias, Elisângela Silva
• Data de Publicação: 2010
• Tipo de documento: Dissertação
• Idioma: por
• Título da fonte: Repositório Institucional da UFG
• dARK ID: ark:/38995/001300000dqh8
• Texto Completo: http://repositorio.bc.ufg.br/tede/handle/tede/12521
• topic: Alianças em grafos; Alianças defensivas; Conjuntos seguros; Alliances in graphs; Defensive alliances; Secure sets; CIENCIAS EXATAS E DA TERRA::CIENCIA DA COMPUTACAO::TEORIA DA COMPUTACAO

A defensive alliance in graph G = (V,E) is a set of vertices S ⊆V satisfying the condition that every vertex v ∈ 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 δ(G), the maximum degree ∆(G), the algebraic connectivity µ, the total dominanting set γt(G), the eccentricity, the edge connectivity λ(G), the chromatic number χ(G), the (vertex) independence number β0(G), the vertex connectivity κ(G), the order of the largest clique ω(G) and the domination number γ(G). It also shows a generalization of defensive alliances, called defensive k alliance, 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”.