of a relativistic star in scalar-tensor theory, following [@de1993]. We restrict ourselves to the static and spherically symmetric case. The metric is given in the following form: $$\label{eq:staticspherical}
  ds_{*}^2 = - e^{\nu(r)}dt^2 + \left(1-\frac{2\mu(r)}{r}
    \right)^{-1}dr^2
  +r^2(d\theta^2+\sin^2 \theta d\phi^2).$$ The matter is described as a perfect fluid: i.e., $$\tilde{T}_{\mu\nu}=(\tilde{\rho}+\tilde{p})\tilde{u}_{\mu}
  \tilde{u}_{\nu}+\tilde{p}\tilde{g}_{\mu\nu}.$$ Then, the following equations are obtained: $$\begin{aligned}
  \label{eq:beq1}
  \mu^{\prime}&=&4\pi G_* r^2 A^4 \tilde{\rho}
  +\frac{1}{2}r(r-2\mu)\psi^2, \\
  \label{eq:beq2}
  \nu^{\prime}&=&8\pi G_* \frac{r^2 A^4 \tilde{p}}{r-2\mu}
  +r\psi^2+\frac{2\mu}{r(r-2\mu)}, \\
  \label{eq:beq3}
  \varphi^{\prime}&=&\psi, \\
  \label{eq:beq4}
  \psi^{\prime}&=&4\pi G_* \frac{r A^4}{r-2\mu}
  [\alpha(\tilde{\rho}-3\tilde{p})+r(\tilde{\rho}-\tilde{p})\psi]
  -\frac{2(r-\mu)}{r(r-2\mu)}\psi, \\
  \label{eq:beq5}
  \tilde{p}^{\prime}&=&-(\tilde{\rho}+\tilde{p})
  \left[4\pi G_*\frac{r^2 A^4 \tilde{p}}{r-2\mu}
    +\frac{1}{2}r\psi^2+\frac{\mu}{r(r-2\mu)}
  +\alpha(\varphi)\psi\right], \\
  \label{eq:beq6}
  \tilde{p}&=&\tilde{p}(\tilde{\rho}),\end{aligned}$$ where the prime denotes a derivative with respect to $r$. We use the polytropic equations of state: $$\begin{aligned}
  \tilde{\rho} &=& \tilde{n}m_b+\frac{Kn_0m_b}{\Gamma-1}
  \left(\frac{\tilde{n}}{n_0}\right)^{\Gamma}, \\
  \tilde{p} &=& Kn_0m_b\left(\frac{\tilde{n}}{n_0}\right)^{\Gamma}, \\
  m_b &=& 1.66\times10^{-24}~\mbox{g}, \\
  n_0 &=& 0.1~\mbox{fm}^{-3},\end{aligned}$$ where $\tilde{n}$ is the baryon number density in the Brans-Dicke frame. We then take the parameters $\Gamma=2.34$ and $K=0.0195$ (EOS II of [@de1993]). Note that the total baryon number is given by $$N=\int 4\pi\tilde{n} A^3 r^2 \left(1-\frac{2\mu}{r}
  \right)^{-1/2}dr.$$

Here we present the method of solving the above equations and obtaining the structure of a neutron star. First the initial values of the above set of ordinary differential equations are fixed as $$\mu 