suborbital graphs
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Author(s):  
Patrick Mwangi Kimani ◽  
Daniel Adicka

Most researchers consider the action of projective general group on the cosets of its maximal subgroups leaving out non-maximal subgroups. In this paper, we consider the action of centralizer of an elliptic element which is a non maximal subgroup . In particular, we determine the subdegrees, rank and properties of the suborbital graphs of the action. We achieve this through the application of the action of a group by conjugation. We have proved that the rank is q  and the subdegrees are  and .



Author(s):  
Wanchai Tapanyo ◽  
Khuanchanok Chaichana
Keyword(s):  


2020 ◽  
Vol 4 (2) ◽  
pp. 82
Author(s):  
Nazlı Yazıcı Gözütok ◽  
Bahadır Özgür Güler

<p>In this paper, we investigate a suborbital graph for the normalizer of Γ<sub>0(<em>N</em>)</sub> ∈ PSL(2;<em>R</em>), where <em>N</em> will be of the form 2<sup>4</sup><em>p</em><sup>2</sup> such that <em>p</em> &gt; 3 is a prime number. Then we give edge and circuit conditions on graphs arising from the non-transitive action of the normalizer.</p>





2020 ◽  
Vol 19 ◽  
pp. 99-106
Author(s):  
Siahi Maxwell Agwanda ◽  
Patrick Kimani ◽  
Ireri Kamuti

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.



2020 ◽  
Vol 57 (3) ◽  
pp. 408-425
Author(s):  
Nazli Yazici Gözütok ◽  
Bahadir Özgür Güler

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.





2020 ◽  
Vol 46 (6) ◽  
pp. 1731-1744
Author(s):  
Yavuz Kesicioğlu ◽  
Mehmet Akbaş
Keyword(s):  


Filomat ◽  
2020 ◽  
Vol 34 (2) ◽  
pp. 631-638
Author(s):  
Seda Öztürk

The Modular group ? is the most well-known discrete group with many applications. This work investigates some subgraphs of the subgroup ?3, defined by {(ab cd)??:ab+cd ?0 (mod 3)}. In [1], the subgraph F1,1 of the subgroup ?3 ? ? is studied, and Fibonacci numbers are obtained by means of the subgraph of F1,1. In this paper, we give a generalization of the subgraphs generating Fibonacci numbers for the subgroup ?3 and some subgraphs having special conditions.



Author(s):  
Khuanchanok Chaichana ◽  
Pradthana Jaipong

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.



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