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Hadron-quark phase transition in neutron star cores is achieved in thepresent work with the help of Maxwell construction. For the purpose we employsix different and well-known hadronic models for the pure hadronic phase. Thequark phase is described with the MIT Bag model in which the density dependenceof the bag pressure $B(\rho)$ is invoked for different asymptotic values($B_{as}$) of $B(\rho)$. The resulting hybrid star (HS) configurations exhibittwin star characteristics and distinct special points (SPs) on the mass-radiusdiagram of the HSs irrespective of the transition densities and the value of$B_{as}$. We find that for any particular value of $B_{as}$, the masscorresponding to SP ($M_{SP}$) and the maximum mass ($M_{max}$) of the HSs,obtained with different hadronic models, follow a nearly linear (fitted)relationship where the slope is independent of the value of $B_{as}$. The$M_{SP}-M_{max}$ dependence of the HSs is found to be consistent with anyhadronic equation of state (EoS) chosen to obtain the hybrid EoS and thus suchrelations can be considered as universal relations in the context of formationof SPs. A change in the value of $B_{as}$ shifts the position of the fittedline in the $M_{SP}-M_{max}$ plane, with the linearity, however, retained.

A Detailed Analysis of the Special Points on $M-R$ Solutions of Hybrid (Twin) Stars