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.
Fibonacci and Lucas numbers of some taxa naturally distributed in North East Anatolia Kuzeydoğu Anadolu'da doğal olarak yayılış gösteren bazı taksonların Fibonacci ve Lucas sayıları
In this study, it is aimed to use the Lorenz matrix multiplication to find the n^th powers of some special matrices and to reach the quadratic equations and characteristic roots of the matrices obtained in this way. In addition, it is aimed to contribute literature to the studies in the field by reaching some identities.
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