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Γ_0 (2^5 p^2) nin normalliyeninin alt yörüngesel graflarındaki dörtgenler

Year 2021, Volume: 11 Issue: 1, 257 - 263, 15.01.2021
https://doi.org/10.17714/gumusfenbil.814413

Abstract

Bu çalışmada, Γ_0 (N) nin PSL(2,R) deki normalliyeni Nor(N) nin alt yörüngesel grafları araştırılmıştır. Burada N pozitif tam sayısı, 2^5 p^2 şeklindeki doğal sayıları ve p sayısı da p>3 şartını sağlayan bir asal sayıyı ifade etmektedir. Nor(N) nin genişletilmiş rasyonel sayılar kümesi Q ̂ üzerindeki hareketinin transitif olmadığı bilinmektedir. Bu transitif olmayan hareketten doğan grafların kenar şartları ve kenar şartları aracılığı ile de alt yörüngesel graflarda ne tür devreler olduğu araştırılmıştır. Yapılan çalışmanın sonucunda bu devrelerin yalnızca dörtgen devreler olacağı elde edilmiştir.

References

  • Akbaş, M. ve Singerman, D. (1992). The signature of the normalizer of Γ_0 (N), London Mathematical Society Lecture Note Series, 165, 77–86.
  • Beşenk, M., Güler, B. Ö. ve Büyükkaya, A. (2019). Suborbital graphs for a non-transitive action of the normalizer, Filomat, 33 (2), 385–392, https://doi.org/10.2298/FIL1902385B
  • Biggs, N. L. ve White, A. T. (1979). Permutation Groups and Combinatorial Structures, Cambridge University Press, Cambridge.
  • Conway, J. H. ve Norton, S. P. (1977). Monstrous moonshine, London Mathematical Society Lecture Note Series, 11, 308–339.
  • Güler, B. Ö., Beşenk, M., Değer, A.H. ve Kader, S. (2011). Elliptic elements and circuits in suborbital graphs, Hacettepe Journal of Mathematics and Statistics, 40(2), 203-210.
  • Güler, B. Ö., Beşenk, M. ve Kader, S. (2019). On congruence equations arising from suborbital graphs, Turkish Journal of Mathematics, 43(5), 2396–2404. https://doi.org/10.3906/mat-1905-93.
  • Güler, B. Ö., Kör, T. ve Şanlı, Z. (2016). Solution to some congruence equations via suborbital graphs, Springerplus, 2016(5), https://doi.org/10.1186/s40064-016-3016-5.
  • Güler, B. Ö. ve Kader, S. (2010). Self-paired edges for the normalizer, Algebras Groups and Geometries, 27(3), 369–376.
  • Jones, G. A., Singerman, D. ve Wicks, K. (1991). The modular group and generalized Farey graphs, London Mathematical Society Lecture Note Series, 160, 316–338. https://doi.org/10.1017/CBO9780511661846.006
  • Kader, S., Güler, B. Ö. ve Akşit, E. (2020). On quadrilaterals in the suborbital graphs of the normalizer, Transactions on Combinatorics, 9(3), 147–159, https://doi.org/10.22108/TOC.2020.120019.1685
  • Kader, S., Güler, B. Ö. ve Deger, A. H. (2010). Suborbital graphs for a special subgroup of the normalizer of Γ_0 (m), Iran. Journal of Science and Technology Transactions A: Science, 34 (4), 305–312.
  • Keskin, R. (2006). Suborbital graphs for the normalizer of Γ_0 (m), European Journal of Combinatorics, 27, 193-206, https://doi.org/10.1016/j.ejc.2004.09.004.
  • Keskin, R. ve Demirtürk, B. (2009). On suborbital graphs for the normalizer Γ_0 (N), The Electronic Journal of Combinatorics, 16, 1-18.
  • Sims, C. C. (1967). Graphs and finite permutation groups, Mathematische Zeitschrift, 95, 76–86, https://doi.org/10.37236/205.
  • Yazıcı Gözütok, N. ve Güler, B. Ö. (2019). Elliptic elements of a subgroup of the normalizer and circuits in orbital graphs, Applications and Applied Mathematics: An International Journal, Special issue 3, 11–21.

Quadrilaterals in the suborbital graphs of the normalizer of Γ_0 (2^5 p^2)

Year 2021, Volume: 11 Issue: 1, 257 - 263, 15.01.2021
https://doi.org/10.17714/gumusfenbil.814413

Abstract

In this paper, we investigate the suborbital graphs for the normalizer of Γ_0 (N) in PSL(2,R), where N will be of the form 2^5 p^2, p is a prime and p > 3. It is known that the action of the normalizer Nor(N) on the extended rational numbers Q ̂ is non transitive. The edge conditions of the graphs arising from this non transitive action and then using these edge conditions, which kind of circuits the suborbital graphs have are investigated. Finally, we show that these circuits are only quadrilaterals.

References

  • Akbaş, M. ve Singerman, D. (1992). The signature of the normalizer of Γ_0 (N), London Mathematical Society Lecture Note Series, 165, 77–86.
  • Beşenk, M., Güler, B. Ö. ve Büyükkaya, A. (2019). Suborbital graphs for a non-transitive action of the normalizer, Filomat, 33 (2), 385–392, https://doi.org/10.2298/FIL1902385B
  • Biggs, N. L. ve White, A. T. (1979). Permutation Groups and Combinatorial Structures, Cambridge University Press, Cambridge.
  • Conway, J. H. ve Norton, S. P. (1977). Monstrous moonshine, London Mathematical Society Lecture Note Series, 11, 308–339.
  • Güler, B. Ö., Beşenk, M., Değer, A.H. ve Kader, S. (2011). Elliptic elements and circuits in suborbital graphs, Hacettepe Journal of Mathematics and Statistics, 40(2), 203-210.
  • Güler, B. Ö., Beşenk, M. ve Kader, S. (2019). On congruence equations arising from suborbital graphs, Turkish Journal of Mathematics, 43(5), 2396–2404. https://doi.org/10.3906/mat-1905-93.
  • Güler, B. Ö., Kör, T. ve Şanlı, Z. (2016). Solution to some congruence equations via suborbital graphs, Springerplus, 2016(5), https://doi.org/10.1186/s40064-016-3016-5.
  • Güler, B. Ö. ve Kader, S. (2010). Self-paired edges for the normalizer, Algebras Groups and Geometries, 27(3), 369–376.
  • Jones, G. A., Singerman, D. ve Wicks, K. (1991). The modular group and generalized Farey graphs, London Mathematical Society Lecture Note Series, 160, 316–338. https://doi.org/10.1017/CBO9780511661846.006
  • Kader, S., Güler, B. Ö. ve Akşit, E. (2020). On quadrilaterals in the suborbital graphs of the normalizer, Transactions on Combinatorics, 9(3), 147–159, https://doi.org/10.22108/TOC.2020.120019.1685
  • Kader, S., Güler, B. Ö. ve Deger, A. H. (2010). Suborbital graphs for a special subgroup of the normalizer of Γ_0 (m), Iran. Journal of Science and Technology Transactions A: Science, 34 (4), 305–312.
  • Keskin, R. (2006). Suborbital graphs for the normalizer of Γ_0 (m), European Journal of Combinatorics, 27, 193-206, https://doi.org/10.1016/j.ejc.2004.09.004.
  • Keskin, R. ve Demirtürk, B. (2009). On suborbital graphs for the normalizer Γ_0 (N), The Electronic Journal of Combinatorics, 16, 1-18.
  • Sims, C. C. (1967). Graphs and finite permutation groups, Mathematische Zeitschrift, 95, 76–86, https://doi.org/10.37236/205.
  • Yazıcı Gözütok, N. ve Güler, B. Ö. (2019). Elliptic elements of a subgroup of the normalizer and circuits in orbital graphs, Applications and Applied Mathematics: An International Journal, Special issue 3, 11–21.
There are 15 citations in total.

Details

Primary Language Turkish
Subjects Engineering
Journal Section Articles
Authors

Nazlı Yazıcı Gözütok 0000-0002-3645-0623

Publication Date January 15, 2021
Submission Date October 21, 2020
Acceptance Date December 23, 2020
Published in Issue Year 2021 Volume: 11 Issue: 1

Cite

APA Yazıcı Gözütok, N. (2021). Γ_0 (2^5 p^2) nin normalliyeninin alt yörüngesel graflarındaki dörtgenler. Gümüşhane Üniversitesi Fen Bilimleri Dergisi, 11(1), 257-263. https://doi.org/10.17714/gumusfenbil.814413