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Year 2016, Volume: 4 Issue: 1, 45 - 54, 15.04.2016
https://doi.org/10.36753/mathenot.421401

Abstract

References

  • [1] Jones, G. A., Singerman, D. and Wicks, K.,The modular group and generalized Farey graphs. London Mathematical Society Lecture Note Series. 160 (1991), 316-338.
  • [2] Akba¸s, M.,On suborbital graphs for the modular group. Bulletin London Mathematical Society. 33 (2001), 647-652.
  • [3] Bigg, N.L. and White, A.T., Permutation groups and combinatorial structures. London Mathematical Society Lecture Note Series 33. Cambridge University Press, Cambridge, 1979.
  • [4] Sims, C.C., Graphs and finite permutation groups. Mathematische Zeitschrift. 95 (1967),76-86.
  • [5] Jones, G. A. and Singerman, D., Complex functions: an algebraic and geometric viewpoint. Cambridge University Press, Cambridge, 1987.
  • [6] Schoeneberg, B., Elliptic modular functions. Springer, Berlin, 1974.
  • [7] Newman, M., Classification of normal subgroups of the modular group.American journal of Mathematics. 126 (1967), 267-277.
  • [8] Tsuzuku, T., Finite Groups and Finite Geometries. Cambridge University Press, Cambridge, 1982.
  • [9] Dixon, J.D. and Mortimer, B., Permutation groups. Springer-Verlag, New York, 1996.
  • [10] Hardy, G.H. and Wright, E.M., An introduction to the theory of numbers. Oxford University Press, Oxford, 1979.
  • [11] Rankin, R.A., Modular forms and functions. Cambridge University Press, Cambridge, 2008.
  • [12] Kesicioğlu, Y., Akba¸s, M. and Beşenk, M., Connectedness of a suborbital graph for congruence subgroups. Journal of Inequalities and Applications. 1 (2013), 117-124.
  • [13] Güler, B.Ö., Beşenk, M., Değer, A.H. and Kader, S., Elliptic elements and circuits in suborbital graphs. Hacettepe Journal of Mathematics and Statistics. 40 (2011),no. 2, 203-210.
  • [14] Beşenk, M., Güler, B.Ö., Değer, A.H. and Kesicioğlu, Y., Circuit lengths of graphs for the Picard gorup. Journal of Inequalities and Applications. 1 (2013), 106-114.

Connectedness of suborbital graphs for a special subgroup of the modular group

Year 2016, Volume: 4 Issue: 1, 45 - 54, 15.04.2016
https://doi.org/10.36753/mathenot.421401

Abstract

In this paper, we investigate connectedness of suborbital graphs for a special congruence subgroups.Firstly,
conditions for being an edge self-paired are provided, then in order to make graph connected, we give
necessary and sufficient conditions for the £u,n, whose vertices form the block [∞].

References

  • [1] Jones, G. A., Singerman, D. and Wicks, K.,The modular group and generalized Farey graphs. London Mathematical Society Lecture Note Series. 160 (1991), 316-338.
  • [2] Akba¸s, M.,On suborbital graphs for the modular group. Bulletin London Mathematical Society. 33 (2001), 647-652.
  • [3] Bigg, N.L. and White, A.T., Permutation groups and combinatorial structures. London Mathematical Society Lecture Note Series 33. Cambridge University Press, Cambridge, 1979.
  • [4] Sims, C.C., Graphs and finite permutation groups. Mathematische Zeitschrift. 95 (1967),76-86.
  • [5] Jones, G. A. and Singerman, D., Complex functions: an algebraic and geometric viewpoint. Cambridge University Press, Cambridge, 1987.
  • [6] Schoeneberg, B., Elliptic modular functions. Springer, Berlin, 1974.
  • [7] Newman, M., Classification of normal subgroups of the modular group.American journal of Mathematics. 126 (1967), 267-277.
  • [8] Tsuzuku, T., Finite Groups and Finite Geometries. Cambridge University Press, Cambridge, 1982.
  • [9] Dixon, J.D. and Mortimer, B., Permutation groups. Springer-Verlag, New York, 1996.
  • [10] Hardy, G.H. and Wright, E.M., An introduction to the theory of numbers. Oxford University Press, Oxford, 1979.
  • [11] Rankin, R.A., Modular forms and functions. Cambridge University Press, Cambridge, 2008.
  • [12] Kesicioğlu, Y., Akba¸s, M. and Beşenk, M., Connectedness of a suborbital graph for congruence subgroups. Journal of Inequalities and Applications. 1 (2013), 117-124.
  • [13] Güler, B.Ö., Beşenk, M., Değer, A.H. and Kader, S., Elliptic elements and circuits in suborbital graphs. Hacettepe Journal of Mathematics and Statistics. 40 (2011),no. 2, 203-210.
  • [14] Beşenk, M., Güler, B.Ö., Değer, A.H. and Kesicioğlu, Y., Circuit lengths of graphs for the Picard gorup. Journal of Inequalities and Applications. 1 (2013), 106-114.
There are 14 citations in total.

Details

Primary Language English
Journal Section Articles
Authors

Murat Beşenk This is me

Publication Date April 15, 2016
Submission Date August 11, 2015
Published in Issue Year 2016 Volume: 4 Issue: 1

Cite

APA Beşenk, M. (2016). Connectedness of suborbital graphs for a special subgroup of the modular group. Mathematical Sciences and Applications E-Notes, 4(1), 45-54. https://doi.org/10.36753/mathenot.421401
AMA Beşenk M. Connectedness of suborbital graphs for a special subgroup of the modular group. Math. Sci. Appl. E-Notes. April 2016;4(1):45-54. doi:10.36753/mathenot.421401
Chicago Beşenk, Murat. “Connectedness of Suborbital Graphs for a Special Subgroup of the Modular Group”. Mathematical Sciences and Applications E-Notes 4, no. 1 (April 2016): 45-54. https://doi.org/10.36753/mathenot.421401.
EndNote Beşenk M (April 1, 2016) Connectedness of suborbital graphs for a special subgroup of the modular group. Mathematical Sciences and Applications E-Notes 4 1 45–54.
IEEE M. Beşenk, “Connectedness of suborbital graphs for a special subgroup of the modular group”, Math. Sci. Appl. E-Notes, vol. 4, no. 1, pp. 45–54, 2016, doi: 10.36753/mathenot.421401.
ISNAD Beşenk, Murat. “Connectedness of Suborbital Graphs for a Special Subgroup of the Modular Group”. Mathematical Sciences and Applications E-Notes 4/1 (April 2016), 45-54. https://doi.org/10.36753/mathenot.421401.
JAMA Beşenk M. Connectedness of suborbital graphs for a special subgroup of the modular group. Math. Sci. Appl. E-Notes. 2016;4:45–54.
MLA Beşenk, Murat. “Connectedness of Suborbital Graphs for a Special Subgroup of the Modular Group”. Mathematical Sciences and Applications E-Notes, vol. 4, no. 1, 2016, pp. 45-54, doi:10.36753/mathenot.421401.
Vancouver Beşenk M. Connectedness of suborbital graphs for a special subgroup of the modular group. Math. Sci. Appl. E-Notes. 2016;4(1):45-54.

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