Projektif Düzlemlerden Elde Edilen Projektif Graflar

Öz

Bu makalede, uzun bir tarihe ve derin teorilere sahip olan iki alanı, graf teorisi ve projektif geometri arasında bir ilişki kurmak için yeni bir metot sunduk. Bu yeni metodu kullanarak sonlu projektif düzlemlerden elde edilen grafların kombinatoryal özelliklerini araştırdık. Aynı zamanda bu kombinatoryal özellikler ile projektif düzlemin mertebesi arasındaki ilişkileri inceledik.

Anahtar Kelimeler

• Projektif düzlemler,Graflar,Köşe derece dizileri

Projective Graphs Obtained from Projective Planes

Öz

In this paper, we introduced a new method to relate two areas, graph theory and projective geometry that have a long history and very deep theories. We investigated the combinatorial properties of the graphs which are obtained from finite projective planes by using this new method. Also, we examined the relations between these combinatorial properties and the order of the projective plane.

Anahtar Kelimeler

• Graphs,Projective planes,Degree sequences

Kaynakça

1. [1] Aigner, M., Triesch, E.: Realizability and uniqueness in graphs, Discrete Math., 136, 3--20 (1994).
2. [2] Barrus, M. D., Donovan, E.: Neighborhood degree lists of graphs, Discrete Math., 341 (1), 175--183 (2018).
3. [3] Bondy A., Murty M. R.: Graph Theory, Springer-Verlag, London, (2008).
4. [4] Cangul. N.: Graf Teori-I, Temel Konular, Dora Yayınları, Bursa, (2017).
5. [5] Choudum, S. A.: On forcibly connected graphic sequences, Discrete Math., 96, 175--181 (1991),
6. [6] Hakimi, S. L.: On the realizability of a set of integers as degrees of the vertices of a graph, J. SIAM Appl. Math., 10, 496-506 (1962).
7. [7] Havel, V.: A remark on the existence of finite graphs (Czech), Casopic Pěst. Mat., 80, 477--480 (1955).
8. [8] Hughes D. R., Piper F. C.: Projective Planes, Springer, New York, (1973).

9. [9] Kaya R., Projektif Geometri, Osmangazi Üniversitesi Yayınları, Eskişehir, 392 s., (2005).
10. [10] Meng K. K., Fengming D. and Guan T. E.: Introduction to Graph Theory H3 Mathematics, World Scientific, (2007).
11. [11] Triphati, A., Venugopalan, S., West, D. B.: A short constructive proof of the Erdös-Gallai characterization of graphic lists, Discrete Math., 310, 843--844 (2010).
12. [12] Tyshkevich, R. I., Chernyak, A. A., Chernyak, Zh. A.: Graphs and degree sequences, Cybernetics, 23 (6), 734--745 (1987).
13. [13] Wallis W. D.: A Beginner’s Guide to Graph Theory, Birkhauser, Boston, (2007).
14. [14] West D. B.: Introduction to Graph Theory, Pearson, India, (2001).
15. [15] Zverovich, I. E., Zverovich, V. E.: Contributions to the theory of graphic sequences, Discrete Math, 105, 293--303 (1992).