Graph Theory: Flows, Matrices [antikvár]

Preface My book Ismerkedés a Gráfelmélettel was published in 1971 and since 1977 it has also been available in English, entitled Introductory Graph Theory. The present book is the continuation of the former at a higher level. It is assumed that the reader has encountered graphs before and is acquainted with some simple results, knows, for example, about trees and routes, and that she or he is able to formulate simple problems in the language of graphs. In short, some inclination and ability is expected of the reader, and even more an intention to gain insight into what is 'behind graphs'. The first chapter is of a preparatory character. Here I show how the structure of graphs is usually characterised from the point of view of various connectivity properties. The second chapter treats flows, transportation and planning problems. Both the possible practical applications and some feasibility considerations are presented. I have devoted the third chapter to the relationship between graphs and matrices. I have made an effort to cover as broad a range of applications as possible. Comprehension of this part requires knowledge of the concept of linear spaces, the basic properties of bases and the operations on matrices. The solution of integro-differential equations is also touched upon in connection with the investigation of electrical networks, but only a glance at the theory of electrical networks is offered; no detailed investigations are carried out. I have endeavoured to write this book with didactical considerations taken into account, and to organise its material to enable the reader aiming at self-reliance to progress on her or his own. Problems have been set at the end of each chapter; their solution is found in the fourth chapter. I promised a continuation in the preface of Introductory Graph Theory, I even outlined some topics to be covered in this book. A glance at the contents reveals that a mere fraction of this plan has been carried out. An important reason is that since the publication of my previous book the internal development of graph theory has witnessed a substantial shift of emphasis in favour of algebraisation. Besides the internal development, the rapid expansion of the range of applications has considerably extended the literature. The applications are primarily from the fields of operations research and of computer