of TM1 (NL3), the maximal pairing gap at the Fermi surface is 0.17 MeV (0.12 MeV), as given in Table II, where ρ$_{B}$ = 0 . 344 fm − 3 ( ρ$_{B}$ = 0 . 303 fm − $^{3}$), Y$_{Λ}$ = 0 . 039 ( Y$_{Λ}$ = 0 . 044), and m ∗ Λ = 743 MeV ( m ∗ Λ = 706 MeV). Takatsuka et al . [24] obtained the maximal pairing gap of 0.34 MeV at ρ$_{B}$ = 4 . 5 ρ$_{0}$ for the TNI6u EOS. The larger pairing gap at higher ρ$_{B}$ given in Ref. [24] is because of their smaller Y$_{Λ}$ and larger m ∗ $_{Λ}$. As discussed in Refs. [20, 23, 24], the pairing gap is very sensitive to the effective mass. Generally, a smaller effective mass leads to a higher single-particle energy and then yields a smaller pairing gap. In Fig. 4, we show the effective mass of Λ hyperons, m ∗ $_{Λ}$, as a function of the baryon density, ρ$_{B}$ , using the RMF model with the TM1 (solid line) and NL3 (dashed line) parameter sets. It is shown that m ∗ Λ decreases with increasing ρ$_{B}$ . When Λ hyperons appear around 0 . 31 fm − 3 (TM1) or 0 . 28 fm − 3 (NL3), the effective mass of Λ hyperons is about 762 MeV or 727 MeV. It is found that the effective masses of Λ hyperons in the NL3 case are smaller than those of TM1, which leads to a smaller pairing gap, as shown in Fig. 2. We note that the effective mass of Λ hyperons is mainly determined by the coupling constants g$_{σ}$$_{Λ}$ and g$_{σ}$ ∗ $_{Λ}$. Here we use the values constrained by reasonable hyperon potentials, which are suggested by the experimental data of single-Λ hypernuclei and by the Nagara event. To examine whether the $^{1}$S$_{0}$ superfluidity of Λ hyperons exists in neutron stars, we solve the Tolman-Oppenheimer-Volkoff (TOV) equation with the EOS of the RMF theory over a wide density range. For the nonuniform matter at low density, which exists in the inner and outer crusts of neutron stars, we adopt a relativistic EOS based on the RMF theory with a local density approximation [7, 36]. The nonuniform matter is modeled to be composed of a lattice of spherical nuclei immersed in an electron gas with or without free neutrons dripping out of nuclei. The low-density EOS is matched to the EOS of uniform matter at the density where they have equal pressure. The neutron star properties are mainly determined by the EOS at high density. Using the EOS described in Sec. II, we calculate the neutron star properties and find that the maximum mass of neutron stars is about 1.70 M ⊙ (2.06 M ⊙ ) with the TM1 (NL3) parameter set. According to the compilation of measured neutron star masses [3, 55], some massive neutron stars were reported to be observed recently. However, the uncertainties in these mass measurements are rather large, and the mass of PSR J0751+1807 was corrected from (2 . 1 ± 0 . 2) M ⊙ to (1 . 26 ± 0 . 14) M ⊙ [56]. We note that the EOS used here could not be ruled out by current observations. In Figs. 5 and 6, we show the central baryon density as a function of the neutron star mass. We find that whether the $^{1}$S$_{0}$ 11