Research Article
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Sirküler grafların temel özellikleri üzerine

Year 2025, Issue: 014, 1 - 6, 30.12.2025

Abstract

Sirküler uzayların çakışım grafları olarak görünen sirküler graflar, projektif geometride herhangi bir ayrık yapının, onu iki parçalı graf modeli olarak tanımlayarak incelenebileceğini kanıtlamıştır. Bu çalışmada, sirküler grafların bazı temel özellikleri incelenerek kısmen sınıflandırılmıştır. Verilen grafların sirküler olup olmadığını Derinlik Öncelikli Arama (DFS) algoritması kullanarak belirleyen Java kaynak kodu verilmiştir.

References

  • [1] A.S. Asratian, T.M.J. Denley and R. Hoggkvist, Bipartite graphs and their applications, Cambridge Uni, United Kingdom. Press,1998.
  • [2] R. Sunar and İ. Günaltılı, “On The Basic Properties of Linear Graphs - I”, Konuralp J. Math., vol. 9, no. 1, pp. 154-158, 2021.
  • [3] İ. Günaltılı, A. Ulukan, and Ş . Olgun, “Some Properties Of Fınıte f0,1g-Graphs” , Konuralp Journal Of Mathematics,1(1), pp. 34-39, 2013.
  • [4] F. Harary, D. Hsu and Z. Miller, “The biparticity of a graph”, J. Graph Theory 1, pp. 131-133, 1977..
  • [5] M. Mulder, “(0, l)-graph and n-cubes”, Discrete mathematics vol. 28, pp. 179-188 1979.
  • [6] D.B. West, “Introduction to Graph Theory”, Prentice-Hall, Englewood Clins, NJ, 1996.
  • [7] C. Vasudev, Combinatorics and Graph Theory, New Age Publications(Academic), India, 2007.
  • [8] L.M. Batten, Combinatorics of finite geometries ,Cambridge University Press, Cambridge-NewYork, 1986.
  • [9] Günaltılı,İ.; Akça,Z. And Olgun,Ş., APPS. Applied Sciences, vol. 8, no. 1, pp. 85-90, 2006.
  • [10] Levi, F. W., 1942, Finite geometrical systems, at the University of Calcutta, University of Calcutta, six public lectues delivered in February, 1940
  • [11] König, D. “Line systems and determinants”, Math. Termész. Ert, vol. 33, pp. 221-229, 1915.
  • [12] König, D., “Über graphen und ihre anwendung auf determinantentheorie und Mengenlehre”. Mathematische Annalen, vol. 77, no. 4, pp. 453-465, 1916.
  • [13] Sorgun,S., Ertaş, A. G., Günaltılı, I., On the incidence graph of circular spaces, Electronic Journal of Graph Theory and Applications, vol. 12, no. 2, pp. 379-386, 2024.

On The Fundamental Properties of Circular Graphs

Year 2025, Issue: 014, 1 - 6, 30.12.2025

Abstract

Circular graphs, which appear as incidence graphs of circular spaces, demonstrate that any discrete structure in projective geometry can be studied by defining it as a bipartite graph model. In this study, circular graphs are partially classified by examining some of their basic properties. Java source code that determines whether the given graphs are circular using the Depth-First Search (DFS) algorithm is provided.

References

  • [1] A.S. Asratian, T.M.J. Denley and R. Hoggkvist, Bipartite graphs and their applications, Cambridge Uni, United Kingdom. Press,1998.
  • [2] R. Sunar and İ. Günaltılı, “On The Basic Properties of Linear Graphs - I”, Konuralp J. Math., vol. 9, no. 1, pp. 154-158, 2021.
  • [3] İ. Günaltılı, A. Ulukan, and Ş . Olgun, “Some Properties Of Fınıte f0,1g-Graphs” , Konuralp Journal Of Mathematics,1(1), pp. 34-39, 2013.
  • [4] F. Harary, D. Hsu and Z. Miller, “The biparticity of a graph”, J. Graph Theory 1, pp. 131-133, 1977..
  • [5] M. Mulder, “(0, l)-graph and n-cubes”, Discrete mathematics vol. 28, pp. 179-188 1979.
  • [6] D.B. West, “Introduction to Graph Theory”, Prentice-Hall, Englewood Clins, NJ, 1996.
  • [7] C. Vasudev, Combinatorics and Graph Theory, New Age Publications(Academic), India, 2007.
  • [8] L.M. Batten, Combinatorics of finite geometries ,Cambridge University Press, Cambridge-NewYork, 1986.
  • [9] Günaltılı,İ.; Akça,Z. And Olgun,Ş., APPS. Applied Sciences, vol. 8, no. 1, pp. 85-90, 2006.
  • [10] Levi, F. W., 1942, Finite geometrical systems, at the University of Calcutta, University of Calcutta, six public lectues delivered in February, 1940
  • [11] König, D. “Line systems and determinants”, Math. Termész. Ert, vol. 33, pp. 221-229, 1915.
  • [12] König, D., “Über graphen und ihre anwendung auf determinantentheorie und Mengenlehre”. Mathematische Annalen, vol. 77, no. 4, pp. 453-465, 1916.
  • [13] Sorgun,S., Ertaş, A. G., Günaltılı, I., On the incidence graph of circular spaces, Electronic Journal of Graph Theory and Applications, vol. 12, no. 2, pp. 379-386, 2024.
There are 13 citations in total.

Details

Primary Language English
Subjects Experimental Mathematics, Applied Mathematics (Other)
Journal Section Research Article
Authors

Ali Gökhan Ertaş 0000-0003-2279-8167

Submission Date August 8, 2025
Acceptance Date September 8, 2025
Publication Date December 30, 2025
Published in Issue Year 2025 Issue: 014

Cite

APA Ertaş, A. G. (2025). On The Fundamental Properties of Circular Graphs. Journal of Scientific Reports-B(014), 1-6.
AMA Ertaş AG. On The Fundamental Properties of Circular Graphs. Journal of Scientific Reports-B. December 2025;(014):1-6.
Chicago Ertaş, Ali Gökhan. “On The Fundamental Properties of Circular Graphs”. Journal of Scientific Reports-B, no. 014 (December 2025): 1-6.
EndNote Ertaş AG (December 1, 2025) On The Fundamental Properties of Circular Graphs. Journal of Scientific Reports-B 014 1–6.
IEEE A. G. Ertaş, “On The Fundamental Properties of Circular Graphs”, Journal of Scientific Reports-B, no. 014, pp. 1–6, December2025.
ISNAD Ertaş, Ali Gökhan. “On The Fundamental Properties of Circular Graphs”. Journal of Scientific Reports-B 014 (December2025), 1-6.
JAMA Ertaş AG. On The Fundamental Properties of Circular Graphs. Journal of Scientific Reports-B. 2025;:1–6.
MLA Ertaş, Ali Gökhan. “On The Fundamental Properties of Circular Graphs”. Journal of Scientific Reports-B, no. 014, 2025, pp. 1-6.
Vancouver Ertaş AG. On The Fundamental Properties of Circular Graphs. Journal of Scientific Reports-B. 2025(014):1-6.