for the hadronic phase. The term q B s is the strange charge baryon B . The strangeness fraction is strongly modified by the different choices of the cutoff. As we can see in Fig. 7, in the case of Λ$_{1}$ with µ$_{0}$ = 400 MeV, the strangeness frac- tion decreases in the mixed phase and increases again in the pure quark matter. However, with µ$_{0}$ = 350 MeV the strangeness fraction increases in the mixed phase and continues to increase in the pure quark matter. For the case of Λ$_{2}$ the strangeness fraction increases in both cases in the mixed phase. These different behaviors are due to the densities at which the mixed phase occurs and the values of the constituent masses of the strange quark for these densities. The Table I shows the values of the con- stituent masses of strange quark on the mixed phase, the value of the densities at the onset of the phase transi- tion, the width of the plateau of the mixed phase and the difference of the strangeness fraction between quark and hadronic phase. The values of the density at the onset of the phase transition and the width of the plateau decrease when µ$_{0}$ decreases for both parametrizations of the cutoff. On the other hand, the discontinuity of the strangeness fraction between the two phases becomes positive and increases. The value of the constituent mass of the s quark generally decreases if µ$_{0}$ decreases except for Λ$_{2}$ with µ$_{0}$ = 350 MeV that has the biggest constituent mass due to the low density at the phase transition density. According to references [11, 12] these results are directly relate with the possible existence of deconfined quark matter in the interior of neutron star as we will see later plateau in the mass versus central density graph. The plateau is a consequence of the Maxwell construction and corresponds to the mixed phase between a pure hadron and a pure quark phase. The cusp occurs at the on- set of the quark phase in the interior of the star. We conclude that for most of the models the deconfinement phase transition makes the star unstable. However, for the cutoff Λ$_{2}$ with µ$_{0}$ = 350 MeV the maximum mass configuration appears after the plateau and the cusp. In this case the star configuration with the maximum mass has a quark phase core. We verify that configurations with a quark phase core are possible only for the chemi- cal potential µ$_{0}$ ≲ 360 MeV. For values of µ$_{0}$ ≳ 360 MeV we have two possibilities: 1) instability of the hybrid star with the onset of a quark phase in the star as we can see in the case of µ$_{0}$ = 400 MeV; 2) the EOS of hadronic phase is favored for all densities if µ$_{0}$ > 430 MeV. We calculate the neutron star configuration for each cutoff solving the Tolman-Oppenheimer-Volkoff (TOV) equations for a spherically symmetric and static star[31, 32]. Fig. 8 shows the gravitational mass of hybrid stars of the maximum mass configuration as a function of (a) the radius and of (b) the central density for each cutoff. As we can see in these plots the maximum mass is influenced by the cutoff. In the Table II we show the values of the gravitational mass, central density and the radius of the maximum mass star configuration constructed with the EOS proposed in the present work as well as with the EOS proposed by Glendenning and Moszkowsky [1, 27]. The gravitational mass of the hybrid stars is charac- terized by a cusp in the mass versus radius plot and a FIG. 8: The gravitational mass of the hybrid star is plotted as a function of a) the star radius and b) the central density, for the different parametrizations of the cutoff. TABLE I: Constituent masses of the strange quark, densities at the onset of the phase transition, width of the plateau of the mixed phases and difference of the strangeness fraction between quark and hadronic phase for each parametrization of the cutoff. FIG. 7: Strangeness fraction r$_{s}$ for different slopes of the cutoff for the quark phase: a) Λ 1 b) Λ 2 . 1 3 5 7 9 / 0 GM1 with hyperons $_{2}$( $_{0}$ = 400 MeV) $_{2}$( $_{0}$ = 350 MeV) 1 3 5 7 9 0 0.1 0.2 0.3 / 0 r s GM1 with hyperons $_{1}$( $_{0}$ = 400 MeV) $_{1}$( $_{0}$ = 350 MeV) b) a) 10 12 14 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 R (km) M/M sun 1 3 5 7 9 1.1 1.2 1.3 1.4 1.5 1.6 1.7 $_{c}$/ 0 M/M sun $_{1}$( $_{0}$ = 400 MeV) $_{1}$( $_{0}$ = 350 MeV) $_{2}$( $_{0}$ = 400 MeV) $_{2}$( $_{0}$ = 350 MeV) b) a) Quark phase Hadron phase Cutoff M$_{s}$ ρ$_{QP}$ Δ ρ Δ r$_{s}$ (MeV) (fm − $^{3}$) (fm − $^{3}$) ( × 10 − $^{2}$) Λ 1 ( µ 0 = 400MeV) 229.16 1.00 0.32 -1.2 Λ 1 ( µ 0 = 350MeV) 225.23 0.82 0.23 2.9 Λ 2 ( µ 0 = 400MeV) 197.27 0.69 0.23 8.2 Λ 2 ( µ 0 = 350MeV) 240.61 0.49 0.14 10.1 6