Suborbital graphs for the group ?2

Amaç & Hipotez:In this paper, we investigate suborbital graphs formed by the action of?2which is the group generated by the second powers of the elementsof the modular group ? on ^Q.

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Temel Bulgular & Veri:Firstly, conditions for being an edge,self-paired and paired graphs are provided, then we give necessary andsufficient conditions for the suborbital graphs to contain a circuit andto be a forest.

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Sonuç & Katkı:Finally, we examine the connectivity of the subgraphFu,Nand show that it is connected if and only if N

🔬Tür:Araştırma Makalesi

📍Kapsam:Genişletilmiş Akademik Örneklem

⚙️Değişkenler:Alan Parametreleri

Abstract

In this paper, we investigate suborbital graphs formed by the action of?2which is the group generated by the second powers of the elementsof the modular group ? on ^Q. Firstly, conditions for being an edge,self-paired and paired graphs are provided, then we give necessary andsufficient conditions for the suborbital graphs to contain a circuit andto be a forest. Finally, we examine the connectivity of the subgraphFu,Nand show that it is connected if and only if N

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Bu Makaleye Atıf Yap

GÜLER, B. Ö., BEŞENK, M., DEĞER, A. H., KESİCİOĞLU, Y. (2022). Suborbital graphs for the group ?2. Hacettepe Journal of Mathematics and Statistics, Cilt: 44 - Sayı: 5, 1033–1044. https://ajindex.com/articles/530271

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Kaynakça (20)

Akbaş, M. and Başkan, T. Suborbital graphs for the normalizer of ?0(N ), Tr. J. of Mathe- matics, 20, 379-387, 1996.
Akbaş, M. On suborbital graphs for the modular group, Bull. London Math. Soc., 33, 647-, 2001.
Beşenk, M. et al. Circuit lengths of graphs for the Picard group, J. Inequal. Appl., 2013:106, pp., 2013.
Bigg, N.L. and White, A.T. Permutation groups and combinatorial structures, London Mathematical Society Lecture Note Series, 33, CUP, Cambridge, 140 pp.,1979.
Dixon, J. D. and Mortimer, B. Permutation Groups, Graduate Texts in Mathematics 163, Springer-Verlag, 1996.
Güler, B.Ö. et al. Elliptic elements and circuits in suborbital graphs, Hacet. J. Math. Stat., (2), 203-210, 2011.
Jones, G.A., Singerman, D. and Wicks, K. The modular group and generalized Farey graphs, London Mathematical Society Lecture Note Series, 160, CUP, Cambridge, 316-338, 1996.
Jones, G.A. and Jones, J.M. Elementary Number Theory, Springer Undergraduate Mathe- matics Series, Springer-Verlag, 1998.
Kader, S., Güler, B. Ö. and Değer, A. H. Suborbital graphs for a special subgroup of the normalizer, IJST. Trans A., 34 (A4), 305-312, 2010.
Kader, S. and Güler, B. Ö. On suborbital graphs for the extended Modular group ^?, Graphs and Combinatorics, 29, no. 6, 1813-1825, 2013.
Keskin, R. Suborbital graphs for the normalizer of ?0(m), European J. Combin., 27, no. 2, 206, 2006.
Neumann, P.M. Finite Permutation Groups, Edge-Coloured Graphs and Matrices, Topics in Group Theory and Computation, Ed. M. P. J. Curran, Academic Press, 1977.
Newman, M. The Structure of some subgroups of the modular group, Illinois J. Math., 6, 487, 1962.
Newman, M. Free subgroups and normal subgroups of the modular group, Illinois J. Math.,, 262-265, 1964.
Newman, M. Classification of normal subgroups of the modular group, Transactions of the American Math. Society, Vol.126, 2, 267-277, 1967.
Rankin, R. A. Modular Forms and Functions, Cambridge University Press, 2008.
Schoeneberg, B. Elliptic modular functions, Springer Verlag, 1974.
Sims, C.C. Graphs and finite permutation groups, Math. Z., 95, 76-86, 1967.
Singerman, D. Subgroups of Fuchsian groups and finite permutation groups, Bull. London Math. Soc., 2, 319-323, 1970.
Tsuzuku, T. Finite Groups and Finite Geometries, Cambridge University Press, Cambridge, 1982.