Circular and octographic graphs in point-line geometry

In this thesis, octographic bipartite graphs in the class of (0, λ)−graphs and bipartite circular graphs obtained from circular spaces are defined. Subsequently, the basic properties of circular and octographic graphs are examined, and their classifications are made. Additionally, in the axiomatic system called point-line geometry, it is shown that the investigation of intersection system structures in finite geometries of any discrete structure is possible with these newly defined bipartite graphs. This study consists of a total of eight sections. The first section includes the introduction and purpose of the thesis, and the second section includes a literature review. In order to contribute significantly to our study and shed light on it, the third section also covers basic concepts. In the fourth section, circular graph is defined, and in the fifth section, the concepts of octographic bipartite graph are defined, and the basic properties of these new bipartite graph types are examined. In addition, the classification of octographic bipartite graphs in this class for the case of λ=1 is done. In the sixth section, an algorithm and computer program that determines the type of given graphs and some basic properties for λ=1 are provided. The seventh section includes findings and discussions, summarizing the obtained results. The final section of our study concludes with results and recommendations.