Thesis (M.S.)--University of Missouri-Columbia, 2003. / Typescript. Includes bibliographical references (leaves 132-133). Also available on the Internet.

Thesis (Ph.D.) - Carleton University, 2007. / Includes bibliographical references (p. 115-129). Also available in electronic format on the Internet.

Thesis (Ph.D.)--Mississippi State University. Department of Mathematics and Statistics. / Title from title screen. Includes bibliographical references.

Thesis (M.S.)--Rochester Institute of Technology, 2006. / Typescript. Includes bibliographical references (leaves 38-39).

Thesis (Ph.D.)--University of Delaware, 2007. / Principal faculty advisor: Errol L. Lloyd, Dept. of Computer & Info Sciences. Includes bibliographical references.

No description available.

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Thesis (MSc (Logistics)--University of Stellenbosch, 2007. / There exists, for any connected graph G, a minimum set of vertices that, when removed, disconnects G. Such a set of vertices is known as a minimum cut-set, the cardinality of which is known as the connectivity number k(G) of G. A connectivity preserving [connectivity reducing, respectively] spanning subgraph G0 ? G may be constructed by removing certain edges of G in such a way that k(G0) = k(G) [k(G0) < k(G), respectively]. The problem of constructing such a connectivity preserving or reducing spanning subgraph of minimum weight is known to be NP–complete. This thesis contains a summary of the most recent results (as in 2006) from a comprehensive survey of literature on topics related to the connectivity of graphs. Secondly, the computational problems of constructing a minimum weight connectivity preserving or connectivity reducing spanning subgraph for a given graph G are considered in this thesis. In particular, three algorithms are developed for constructing such spanning subgraphs. The theoretical basis for each algorithm is established and discussed in detail. The practicality of the algorithms are compared in terms of their worst-case running times as well as their solution qualities. The fastest of these three algorithms has a worst-case running time that compares favourably with the fastest algorithm in the literature. Finally, a computerised decision support system, called Connectivity Algorithms, is developed which is capable of implementing the three algorithms described above for a user-specified input graph.

Thesis (MSc (Mathematical Sciences. Applied Mathematics))--University of Stellenbosch, 2007. / In this thesis we focus on the lower domination parameters of a graph G, denoted ¼(G), for ¼ 2 {i, ir, °}. For each of these parameters, we are interested in characterizing the structure of graphs that are critical when faced with small changes such as vertex-removal, edge-addition and edge-removal. While criticality with respect to independence and domination have been well documented in the literature, many open questions still remain with regards to irredundance. In this thesis we answer some of these questions. First we describe the relationship between transitivity and criticality. This knowledge we then use to determine under which conditions certain classes of graphs are critical. Each of the chosen classes of graphs will provide specific examples of different types of criticality. We also formulate necessary conditions for graphs to be ir-critical and ir-edge-critical.

Submitted by FLAVIA FERNANDA FAVARO null (flaviafavaro@hotmail.com) on 2018-01-10T03:14:21Z No. of bitstreams: 1 A Teoria dos Grafos e sua abordagem na sala de aula com recursos educacionais digitais.pdf: 2731904 bytes, checksum: 49a548fa505952226f589c5471f9b496 (MD5) / Approved for entry into archive by Adriana Aparecida Puerta null (dripuerta@rc.unesp.br) on 2018-01-10T18:21:25Z (GMT) No. of bitstreams: 1 favaro_ff_me_rcla.pdf: 2692020 bytes, checksum: c889310c873cab619e98b36f809e81c0 (MD5) / Made available in DSpace on 2018-01-10T18:21:25Z (GMT). No. of bitstreams: 1 favaro_ff_me_rcla.pdf: 2692020 bytes, checksum: c889310c873cab619e98b36f809e81c0 (MD5) Previous issue date: 2017-12-18 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / Neste trabalho estudamos a Teoria dos Grafos compreendendo suas definições, resultados e algumas aplicações como O Problema das Pontes de Köningsberg, O Problema Chinês do Carteiro, O Problema do Caixeiro Viajante e O Teorema das Quatro e das Cinco Cores. Com o uso da Coleção M3 - Matemática Multimídia, que contém recursos educacionais em formatos digitais, aplicamos as atividades sugeridas aos alunos do segundo ano do Ensino Médio de uma escola particular localizado na cidade de São Pedro - SP. As atividades mostraram que, apesar da Teoria dos Grafos não constar no currículo regular do Ensino Médio, sua aplicação para este grupo de alunos foi positiva, uma vez que os alunos sentiram-se motivados com o conteúdo abordado na forma digital e com sua aplicação ao estudo de Matrizes. Concluímos assim que, nos dias atuais a ligação do processo de ensino aprendizagem com os softwares educacionais podem proporcionar, tanto para os professores quanto para os alunos, uma forma mais prazerosa e eficaz de obter conhecimento em Matemática. / In this work, we study Graph Theory, meaning its definitions, results e some applications such as the Köningsberg bridge problem, the chinese postman problem, the travelling salesman problem and the four color theorem as well as the five color theorem. By using the M3 - Matemática Multimídia Series, which contains educational resources in digital form, we applied the suggested activities to second year high school students form a private school located at the city of São Pedro – São Paulo State. The activities showed that, although Graph Theory is not part of the high school regular curriculum, its application to this group of students was positive, since the students felt themselves motivated by the digital approach to its contents and its applications to the study of Matrices. We conclude that, nowadays, the connection between the teaching processes and educational softwares can provide, to the teachers as well as to the students, a more pleasurable and efficient way to obtain knowledge in Mathematics.