Vertices of Suborbital Graph $F_{u,N}$ under Lorentz Matrix Multiplication

In this study, suborbital graphs, $G_{u,N}$ and $F_{u,N}$ are examined. Modular group $\Gamma$ its act on $\widehat{\mathbb{Q}}$ studied. Lorentz matrix that gives the vertices obtained under classical multiplication in graph is analysed with multiplication. written as Möbius transform normalized type of researched. Moreover, a different element scrutinized. The path starting $\infty$ For path, it shown satisfied farthest vertex condition for previous vertex.