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In this paper, we examine some properties of suborbital graphs for the group SL (3 ; Z ). We first, introduce an invariant equivalence relation by using the congruence subgroup SL (3 ; Z ) instead of Gamma 0 ( n ) and obtain some results for the newly constructed subgraphs F u ; n whose vertices form the block [ 1 ]. We obtain edge and circuit conditions and some relations between lengths of circuits in F u ; n and elliptic elements of Gamma 0 ( n ).

Suborbital graphs for a special subgroup of the SL(3,Z)