Oriented graphs

In this thesis, directed graphs which form the most interesting type of graphs with a large application area are studied. In many graphs like electrical circuits, there may be one way relations between the vertices modelling things in the problem and in such cases, directed graphs are used instead of graphs. This thesis consists of 8 chapters. The first chapter is the introductory chapter and the fundamental notions are recalled here together with the results which will be needed in later chapters. Also some frequently used graph classes and their fundamental properties are given. In the second chapter, the notion of directed graphs are considered. Further, the oriented, labeled and unlabeled graphs are recalled. In the third chapter, the characteristic polynomials of directed graphs are studied. While characteristic polynomials of classical graphs consists of 0 and 1s, the characteristic polynomials of directed graphs consists of 0, 1 and -1s. In the fourth and fifth chapters, characteristic polynomials of directed and oriented graphs are studied. In the sixth and seveth chapters, the effects of edge addition and similar operations on characteristic polynomials and the effects of joining or seperating graphs are studied. In the eighth and last chapter, some conclusions are summarized.