Graphs and Networks. Basic Theory and Algorithms - by JMS Simões Pereira

This book aims to give an introduction to Graph and Network Theory and can be used by anyone who does not have the slightest notion of this important area of ​​Mathematics. This importance is mainly due to the numerous and varied applications in Sciences and Technologies apparently distant from traditional Mathematics. 6 chapters, the book deals successively with basic definitions, fundamental structures, Euler and Hamilton-Kirkman paths, planarity and duality, relationships between graphs and matrices, finally, valued graphs (or networks) Includes the most used algorithms since the classics on flows and optimization of routes to those that regulate a traffic light system All demonstrations are presented in detail and the bibliography exceeds 200 items For the 118 or 151 counting by lines proposed problems are suggested resolutions The author published in Portugal an edition entitled Discrete Mathematics: Graphs , Networks, Applications (Editora Luz da Vida, 2009), much more voluminous, in which, in addition to these same subjects, advanced topics are treated such as the relationships between graphs and vector spaces, matroids, topologies, groups, categories and respective applications. Eventually, they may constitute another volume to be published in Brazil.