scholarly journals Chromatic Numbers of Suborbital Graphs for the Modular Group and the Extended Modular Group

2017 ◽  
Vol 2017 ◽  
pp. 1-7
Author(s):  
Wanchai Tapanyo ◽  
Pradthana Jaipong
Keyword(s):  
Modular Group ◽  
Chromatic Numbers ◽  
Suborbital Graphs ◽  
Forest Conditions ◽  
Research Studies

This research studies the chromatic numbers of the suborbital graphs for the modular group and the extended modular group. We verify that the chromatic numbers of the graphs are2or3. The forest conditions of the graphs for the extended modular group are also described in this paper.

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.

scholarly journals Directed suborbital graphs on the Poincare disk

2018 ◽  
pp. 555-560
Keyword(s):  
Modular Group ◽  
Congruence Subgroup ◽  
Directed Graphs ◽  
Suborbital Graphs ◽  
Poincaré Disk ◽  
Special Congruence

In this paper we investigate suborbital graphs of a special congruence subgroup of modular group. And this directed graphs is drawn in Poincare disk.

On Suborbital Graphs for the Extended Modular Group $${\hat{\Gamma}}$$

2012 ◽  
Vol 29 (6) ◽  
pp. 1813-1825 ◽  
Author(s):  
Serkan Kader ◽  
Bahadır Özgür Güler
Keyword(s):  
Modular Group ◽  
Suborbital Graphs

ON SUBORBITAL GRAPHS FOR THE MODULAR GROUP

2001 ◽  
Vol 33 (6) ◽  
pp. 647-652 ◽  
Author(s):  
M. AKBAS
Keyword(s):  
Modular Group ◽  
Suborbital Graphs ◽  
Suborbital Graph

This paper proves a conjecture of G. A. Jones, D. Singerman and K. Wicks, that a suborbital graph for the modular group is a forest if and only if it contains no triangles.

scholarly journals Suborbital graphs of a power subgroup of the modular group

2018 ◽  
Vol 1 (6) ◽  
pp. 139-144 ◽  
Author(s):  
Zeynep Şanli ◽  
Tuncay Köroğlu ◽  
Bahadir Özgür Güler
Keyword(s):  
Modular Group ◽  
Suborbital Graphs

scholarly journals A generalization of the suborbital graphs generating Fibonacci numbers for the subgroup Г3

Filomat ◽  
2020 ◽  
Vol 34 (2) ◽  
pp. 631-638
Author(s):  
Seda Öztürk
Keyword(s):  
Modular Group ◽  
Discrete Group ◽  
Fibonacci Numbers ◽  
Suborbital Graphs

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.

Conducting Dysphagia Research in the Field Through Partnerships With Clinicians

2011 ◽  
Vol 20 (2) ◽  
pp. 36-41
Author(s):  
Catriona M. Steele
Keyword(s):  
Dysphagia Research ◽  
Research Studies

Research studies that involve collaborations between scientists and frontline clinicians provide rich opportunities for advancing knowledge in the field of dysphagia. However, various challenges exist in bridging research goals and clinical priorities. In this article, we explore the perspectives of those who have participated in previous collaborations to gain insights regarding the challenges, surprises, and benefits of such collaboration.

Mother-to-child transmission of HIV: developing integration of healthcare programmes with clinical, social and basic research studies

2003 ◽  
Vol 92 (11) ◽  
pp. 1343-1348
Author(s):  
Menu E ◽  
Scarlatti G ◽  
Barré-Sinoussi F ◽  
Gray G ◽  
Bollinger B ◽  
...  
Keyword(s):  
Basic Research ◽  
Mother To Child Transmission ◽  
Child Transmission ◽  
Mother To Child ◽  
Research Studies
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