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Recently, it has been supposed that the Einstein-Gauss- Bonnet theory coupledwith scalar field (EGBS) maybe appropriately admit physically viable models ofcelestial phenomena such that the scalar field effect is active in standardfour dimensions. We consider the spherically symmetric and static configurationof the compact star and explain the consequences of the EGBS theory in theframe of stellar modeling. In our formulation, for any given static profile ofthe energy density $\rho$ with the spherical symmetry and the arbitraryequation of state (EoS) of matter, we can construct the model which reproducesthe profile. Because the profile of the energy density determines the mass $M$and the radius $R_s$ of the compact star, an arbitrary relation between themass $M$ and the radius $R_s$ of the compact star can be realized by adjustingthe potential and the coefficient function of the Gauss-Bonnet term in theaction of EGBS theory. This could be regarded as a degeneracy between the EoSand the functions characterizing the model, which tells that only themass-radius relation is insufficient to constrain the model. For example, weinvestigate a novel class of analytic spherically symmetric interior solutionsby the polytropic EoS. We discuss our model in detail and show that it is inagreement with the necessary physical conditions required for any realisticcompact star approving that EGBS theory is consistent with observations.

Isotropic compact stars in 4-dimensional Einstein-Gauss-Bonnet gravity coupled with scalar field -- Reconstruction of model