Let K be an unramified quadratic extension of Q_p for a fixed p > 2. Projective general linear groups G = PGL(2,K) and H = PGL(2,Q_p) act transitively on Bruhat-Tits trees T_G and T_H , respectively. We showed the rigidity of H-orbits in ΓG when Γ is a Schottky subgroup of G which gives a graph ΓT_G infinite volume under certain additional conditions