Hexagonal cell graphs of the normalizer with signature $(2, 6, \infty)$

Abstract

In this paper, we investigate suborbital graphs G u,n of the normalizer Γ B (N ) of Γ 0 (N ) in P SL(2, R) for N = 2 α 3 β , where α = 0, 2, 4, 6 and β = 1, 3. In each of these cases, the normalizer becomes a triangle group and the graph arising from the action of the normalizer contains hexagonal circuits. In order to obtain graphs, we first define an imprimitive action of Γ B (N ) on Q using the group H B (N ) and then we obtain some properties of the graphs arising from this action.

Normalizer Maps Modulo N

“…Many researchers have conducted studies [2][3][4][5][6][7] that reveal the relationship of many groups of graphswith the methods and results presented in this study. In particular, because of the interesting nature of the normalizer Γ B (N) of Γ 0 (N) in PSL(2, R) [8][9][10] and its complexity relative to the modular group, researchers have studied normalizer-related graphs under various conditions [2,[11][12][13].…”