Yıl: 2022 Cilt: 51 Sayı: 3 Sayfa Aralığı: 666 - 679 Metin Dili: İngilizce DOI: 10.15672/hujms.824436 İndeks Tarihi: 11-04-2023

Hexagonal cell graphs of the normalizer with signature (2,6,∞)

Öz:
In this paper, we investigate suborbital graphs Gu,n of the normalizer ΓB(N) of Γ0(N) in PSL(2,R) for N = 2α3β, where α = 0,2,4,6 and β = 1,3. In each of these cases, the normalizer becomes a triangle group and the graph arising from the action of the normalizer contains hexagonal circuits. In order to obtain graphs, we first define an imprimitive action of ΓB (N ) on Qb using the group HB (N ) and then we obtain some properties of the graphs arising from this action.
Anahtar Kelime: normalizer suborbital graph hexagon

Belge Türü: Makale Makale Türü: Araştırma Makalesi Erişim Türü: Erişime Açık
  • [1] M. Akbaş and D. Singerman, The signature of the normalizer of Γ0(N ) in P SL(2, R), London Math. Soc. 165, 77–86, 1992.
  • [2] N.L. Biggs and A.T. White, Permutation groups and combinatorial structures, Lon- don Math. Soc. Lec. Not. Ser., 33rd ed. CUP, Cambridge, 1979.
  • [3] I.N. Cangül and D. Singerman, Normal subgroups of Hecke groups and regular maps, Math. Proc. Camb. Phil. Soc. 123, 59–74, 1998.
  • [4] K.S. Chua and M.L Lang, Congruence subgroups associated to the monster, Experi- ment. Math. 13 (3), 343–360, 2004.
  • [5] J.H. Conway and S.P. Norton, Monstrous Moonshine, Bull. London Math. Soc. 11, 308–339, 1977.
  • [6] H.S.M. Coxeter and W.O.F. Moser, Generators and Relations for Discrete Groups, 4th ed. Springer-Verlag, 1984.
  • [7] H.M. Farkas and I. Kra, Theta constants, Riemann surfaces and the modular group, Graduate Texts in Mathematics, 37, AMS, 2001.
  • [8] B.Ö. Güler, M. Beşenk and S. Kader, On congruence equations arising from suborbital graphs, Turk. J. Math. 43 (5), 2396–2404, 2019.
  • [9] I. Ivrissimtzis, D. Singerman and J. Strudwick, From farey fractions to the Klein quartic and beyond, Ars Math. Comtemp. 20 (1), 37–50, 2021.
  • [10] G.A. Jones and D. Singerman, Theory of maps on orientable surfaces, Proc. London Math. Soc. 37 (3), 273–307, 1978.
  • [11] I. Ivrissimtzis and D. Singerman, Regular maps and principal congruence subgroups of Hecke groups, Eur. J. Comb. 26, 437–456, 2005.
  • [12] G.A. Jones and D. Singerman, Complex Functions, an Algebraic and Geometric View- point, CUP, 1987.
  • [13] S. Kader, Circuits in suborbital graphs for the normalizer, Graphs Combin. 33 (6), 1531–1542, 2017.
  • [14] C. Maclachlan, Groups of units of zero ternary quadratic forms, Proc. Royal Soc. 88(A), 141-157, Edinburgh, 1981.
  • [15] C.C. Sims, Graphs and finite permutation groups, Math. Z. 95, 76-86, 1967.
  • [16] D. Singerman, Universal tessellations, Rev. Mat. Univ. Complut. 1, 111–123, 1988.
  • [17] D. Singerman and J. Strudwick, Petrie polygons, Fibonacci sequences and Farey maps, Ars Math. Contemp. 10 (2), 349–357, 2016.
  • [18] D. Singerman and J. Strudwick, The Farey maps modulo n, Acta Math. Univ. Comen. 89 (1), 39–52, 2020.
  • [19] J. Siran, How symmetric can maps on surfaces be?, Surveys in Combinatorics, 161– 238, London Math. Soc. Lec. Not. Ser. 409, CUP, Cambridge, 2013.
  • [20] N. Yazıcı Gözütok, U. Gözütok and B.Ö. Güler, Maps corresponding to the subgroups Γ0(N ) of the modular group, Graphs Combin. 35 (6), 1695–1705, 2019.
  • [21] N. Yazıcı Gözütok and B.O. Güler, Quadrilateral cell graphs of the normalizer with signature (2, 4, ∞), Stud. Sci. Math. Hung. 57 (3), 408–425, 2020.
APA Yazıcı Gözütok N, GÜLER B (2022). Hexagonal cell graphs of the normalizer with signature (2,6,∞). , 666 - 679. 10.15672/hujms.824436
Chicago Yazıcı Gözütok Nazlı,GÜLER BAHADIR OZGÜR Hexagonal cell graphs of the normalizer with signature (2,6,∞). (2022): 666 - 679. 10.15672/hujms.824436
MLA Yazıcı Gözütok Nazlı,GÜLER BAHADIR OZGÜR Hexagonal cell graphs of the normalizer with signature (2,6,∞). , 2022, ss.666 - 679. 10.15672/hujms.824436
AMA Yazıcı Gözütok N,GÜLER B Hexagonal cell graphs of the normalizer with signature (2,6,∞). . 2022; 666 - 679. 10.15672/hujms.824436
Vancouver Yazıcı Gözütok N,GÜLER B Hexagonal cell graphs of the normalizer with signature (2,6,∞). . 2022; 666 - 679. 10.15672/hujms.824436
IEEE Yazıcı Gözütok N,GÜLER B "Hexagonal cell graphs of the normalizer with signature (2,6,∞)." , ss.666 - 679, 2022. 10.15672/hujms.824436
ISNAD Yazıcı Gözütok, Nazlı - GÜLER, BAHADIR OZGÜR. "Hexagonal cell graphs of the normalizer with signature (2,6,∞)". (2022), 666-679. https://doi.org/10.15672/hujms.824436
APA Yazıcı Gözütok N, GÜLER B (2022). Hexagonal cell graphs of the normalizer with signature (2,6,∞). Hacettepe Journal of Mathematics and Statistics, 51(3), 666 - 679. 10.15672/hujms.824436
Chicago Yazıcı Gözütok Nazlı,GÜLER BAHADIR OZGÜR Hexagonal cell graphs of the normalizer with signature (2,6,∞). Hacettepe Journal of Mathematics and Statistics 51, no.3 (2022): 666 - 679. 10.15672/hujms.824436
MLA Yazıcı Gözütok Nazlı,GÜLER BAHADIR OZGÜR Hexagonal cell graphs of the normalizer with signature (2,6,∞). Hacettepe Journal of Mathematics and Statistics, vol.51, no.3, 2022, ss.666 - 679. 10.15672/hujms.824436
AMA Yazıcı Gözütok N,GÜLER B Hexagonal cell graphs of the normalizer with signature (2,6,∞). Hacettepe Journal of Mathematics and Statistics. 2022; 51(3): 666 - 679. 10.15672/hujms.824436
Vancouver Yazıcı Gözütok N,GÜLER B Hexagonal cell graphs of the normalizer with signature (2,6,∞). Hacettepe Journal of Mathematics and Statistics. 2022; 51(3): 666 - 679. 10.15672/hujms.824436
IEEE Yazıcı Gözütok N,GÜLER B "Hexagonal cell graphs of the normalizer with signature (2,6,∞)." Hacettepe Journal of Mathematics and Statistics, 51, ss.666 - 679, 2022. 10.15672/hujms.824436
ISNAD Yazıcı Gözütok, Nazlı - GÜLER, BAHADIR OZGÜR. "Hexagonal cell graphs of the normalizer with signature (2,6,∞)". Hacettepe Journal of Mathematics and Statistics 51/3 (2022), 666-679. https://doi.org/10.15672/hujms.824436