Research Article
Year 2022,
Issue: 41, 35 - 50, 31.12.2022
Abstract
In this study, suborbital graphs, $G_{u,N}$ and $F_{u,N}$ are examined. Modular group $\Gamma$ and its act on $\widehat{\mathbb{Q}}$ are studied. Lorentz matrix that gives the vertices obtained under the classical matrix multiplication in the suborbital graph $F_{u,N}$ is analysed with the Lorentz matrix multiplication. Lorentz matrix written as Möbius transform is normalized and the type of the transform is researched. Moreover, a different element of Modular group $\Gamma$ is scrutinized. The vertices on the path starting with $\infty$ are obtained under this element and the Lorentz matrix multiplication. For this path, it is shown that the vertices obtained in $F_{u,N}$ under the Lorentz matrix multiplication with the Lorentz matrix satisfied the farthest vertex condition for the previous vertex.
References
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Year 2022,
Issue: 41, 35 - 50, 31.12.2022
Abstract
References
- C. C. Sims, Graphs and Finite Permutation Groups, Mathematische Zeitschrift 95 (1967) 76–86.
- P. M. Neumann, Finite Permutation Groups, Edge Coloured Graphs and Matrices, Topics in Group Theory and Computation, Academic Press, London, 1977.
- T. Tsukuzu, Finite Groups and Finite Geometries, Cambridge University Press, Cambridge, 1982.
- G. A. Jones, D. Singerman, K. Wicks, The Modular Group and Generalized Farey Graphs, London Mathematical Society Lecture Note Series 160 (1991) 316–338.
- M. Akbaş, On Suborbital Graphs for Modular Group, Bulletin of the London Mathematical Society 33 (2001) 647–652. B. Ö. Güler, M. Beşenk, A. H. Değer, S. Kader, Elliptic Elements and Circuits in Suborbital Graphs, Hacettepe Journal of Mathematics and Statistics 40 (2011) 203–210.
- A. H. Değer, Vertices of Paths of Minimal Lengths on Suborbital Graphs, Filomat 31 (4) (2017) 913–923.
- M. Beşenk, Suborbital Graphs for the Invariance Group, Beykent University Journal of Science and Engineering 10 (2017) 15–29.
- A. H. Değer, Relationships with the Fibonacci Numbers and the Special Vertices of the Suborbital Graphs, Gümüşhane University Journal of Science and Technology 7 (2017) 168–200.
- H. Gündoğan, O. Keçilioğlu, Lorentzian Matrix Multiplication and the Motions on Lorentzian Plane, Glasnik Matematicki 41 (61) (2006) 329–334.
- T. Koshy, Fibonacci and Lucas Numbers with Applications, Wiley-Interscience Publication, New York, 2001.
- A. H. Değer, M. Beşenk, B. Ö. Güler, On Suborbital Graphs and Related Continued Fractions, Applied Mathematics and Computation 218 (3) (2011) 746–750.
- J. G. Ratcliffe, Foundations of Hyperbolic Manifolds, Springer-Verlag, New York, 1994.
- H. Gündoğan, O. Keçilioğlu, Pseudo Matrix Multiplication, Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 66 (2) (2017) 37–43.
There are 13 citations in total.
Details
| Primary Language | English |
|---|---|
| Subjects | Mathematical Sciences |
| Journal Section | Research Article |
| Authors | |
| Publication Date | December 31, 2022 |
| Submission Date | August 13, 2022 |
| Published in Issue | Year 2022 Issue: 41 |
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