Graf teorisinde pozitif tanımlı tamamlama problemi

The main source used in the preparation of this thesis is the graduate textbook "Graphs and Matrices", Bapat (2014). Essentially, what we do is to study the twelfth chapter of the mentioned textbook to understand and explain the "positive definite completion problem in graph theory", as can be understood from the title of the thesis. But of course, no part of the aforementioned book has been quoted exactly, a study has been put forward with our own words and our own sentences; almost every proof has been written in more detail, and parts of the book that were left to the reader have been explained completely and the subject has been presented more understandably. In addition to these, the sources listed in the references were also consulted. Especially, for the preparation of chapter one, we benefited greatly from Paziak and Odell (2007). To summarize: In the first chapter, preliminaries about matrix theory, which are needed to understand the thesis, are given. In the second and main chapter of the thesis, chordal graphs are defined, positive definite completion notion is given, and it is proved that a graph is positive definite completable if and only if it is chordal. In the third chapter, the last chapter before the conclusions and recommendation chapter, a brief literature review on the subject of the thesis is presented mainly by using the notes at the end of the twelfth chapter of the mentioned book.