Imprimitive action of the normalizer of Γ0(N) and suborbital graphs

2015 ◽  
Author(s):  
Ali Hikmet Değer
Keyword(s):  
Suborbital Graphs ◽  
Imprimitive Action

Quadrilateral cell graphs of the normalizer with signature (2,4,∞)

2020 ◽  
Vol 57 (3) ◽  
pp. 408-425
Author(s):  
Nazli Yazici Gözütok ◽  
Bahadir Özgür Güler
Keyword(s):  
Triangle Group ◽  
Suborbital Graphs ◽  
Imprimitive Action

AbstractIn this study, we investigate suborbital graphs Gu,n of the normalizer ΓB (N) of Γ0 (N) in PSL(2, ℝ) for N = 2α3β where α = 1, 3, 5, 7, and β = 0 or 2. In these cases the normalizer becomes a triangle group and graphs arising from the action of the normalizer contain quadrilateral circuits. In order to obtain graphs, we first define an imprimitive action of ΓB (N) on using the group (N) and then obtain some properties of the graphs arising from this action.

scholarly journals Solutions to some congruence equations via suborbital graphs

SpringerPlus ◽  
2016 ◽  
Vol 5 (1) ◽  
Author(s):  
Bahadır Özgür Güler ◽  
Tuncay Kör ◽  
Zeynep Şanlı
Keyword(s):  
Suborbital Graphs

scholarly journals On congruence equations arising from suborbital graphs

2019 ◽  
Vol 43 (5) ◽  
pp. 2396-2404 ◽  
Author(s):  
Bahadır Özgür GÜLER ◽  
Murat BEŞENK ◽  
Serkan KADER
Keyword(s):  
Suborbital Graphs

scholarly journals Infinite Paths of Minimal Length on Suborbital Graphs for Some Fuchsian Groups

2019 ◽  
Vol 2019 ◽  
pp. 1-8
Author(s):  
Khuanchanok Chaichana ◽  
Pradthana Jaipong
Keyword(s):  
Prime Number ◽  
Fuchsian Group ◽  
Continued Fraction ◽  
Sufficient Conditions ◽  
Minimal Length ◽  
Necessary And Sufficient Conditions ◽  
Fuchsian Groups ◽  
Suborbital Graphs ◽  
Necessary And Sufficient ◽  
Recursive Representation

In this study, we work on the Fuchsian group Hm where m is a prime number acting on mℚ^ transitively. We give necessary and sufficient conditions for two vertices to be adjacent in suborbital graphs induced by these groups. Moreover, we investigate infinite paths of minimal length in graphs and give the recursive representation of continued fraction of such vertex.

scholarly journals On suborbital graphs for some Hecke groups

2001 ◽  
Vol 234 (1-3) ◽  
pp. 53-64 ◽  
Author(s):  
Refik Keskin
Keyword(s):  
Hecke Groups ◽  
Suborbital Graphs

scholarly journals Ranks, Subdegrees and Suborbital graphs of the product action of Affine Groups

2020 ◽  
Vol 19 ◽  
pp. 99-106
Author(s):  
Siahi Maxwell Agwanda ◽  
Patrick Kimani ◽  
Ireri Kamuti
Keyword(s):  
Direct Product ◽  
Cartesian Product ◽  
Galois Field ◽  
Suborbital Graphs ◽  
Affine Groups ◽  
Product Action ◽  
Definition Of ◽  
Suborbital Graph

The action of affine groups on Galois field has been studied.  For instance,  studied the action of on Galois field for  a power of prime.  In this paper, the rank and subdegree of the direct product of affine groups over Galois field acting on the cartesian product of Galois field is determined. The application of the definition of the product action is used to achieve this. The ranks and subdegrees are used in determination of suborbital graph, the non-trivial suborbital graphs that correspond to this action have been constructed using Sims procedure and were found to have a girth of 0, 3, 4 and 6.

scholarly journals Vertices of paths of minimal lengths on suborbital graphs

Filomat ◽  
2017 ◽  
Vol 31 (4) ◽  
pp. 913-923 ◽  
Author(s):  
Ali Değer
Keyword(s):  
Modular Group ◽  
Rational Numbers ◽  
Suborbital Graphs

The Modular group ? acts on the set of extended rational numbers ?Q transitively. Here, our main purpose is to examine some properties of hyperbolic paths of minimal lengths in the suborbital graphs for ?. We characterize all vertices of these hyperbolic paths in the suborbital graphs which are trees.

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