Suborbital graphs of the congruence subgroup Γ(N)

Abstract

© 2018, The Managing Editors. In this paper, for any positive integer N, we determine the edge conditions of suborbital graphs for the congruence subgroup Γ0(N),Gp,q, and the suborbital graph of the block [∞] , F p,q , which is a subgraph of G p,q . Then we give the necessary and sufficient conditions for graphs to contain a triangle, which eventually leads to the conditions for it to be a forest.