rate of the neutrino signals emitted from a SN using a water-[Č]{}erenkov detector of Super-Kamiokande (SK). The positron energy spectrum of the rate of neutrino event $i$ is evaluated to be $$\begin{aligned}
\frac{d^2N_i}{dE_e dt} &=& \nonumber
\frac{N_{{\rm target},i}}{4 \pi d^2} \eta({E_e}) \\ \nonumber
&\times& \sum_{\beta} \int_{0}^{\infty}
\frac{d^2N_{\nu_\beta}}{dE_\nu dt}
P_{\nu_\beta \rightarrow \nu_\alpha}(E_\nu)
\sigma_{\nu_{\alpha} i}(E_\nu) \\
&\times& \left( \frac{dE_\nu}{dE_e'}\right)_i
R(E_e, E_e') dE_e' ,\end{aligned}$$ where $N_{{\rm target},i}$ is the number of the target for reaction $i$, $d$ is the distance from a SN, $\eta(E_e)$ is the detection efficiency, $d^2N_{\nu_\beta}/dE_\nu dt$ is the $\nu_\beta$ number rate per neutrino energy per time, $P_{\nu_\beta \rightarrow \nu_\alpha}(E_\nu)$ is the transition probability from $\nu_\beta$ to $\nu_\alpha$ with the energy $E_\nu$ through neutrino oscillations, $\sigma_{\nu_\alpha i}(E_\nu)$ is the cross section of $\nu_\alpha$ neutrino reaction $i$, $(dE_\nu/dE_e')_i$ is the derivative of the incident neutrino energy on the emitted positron energy for reaction $i$, $R(E_e, E_e')$ is the energy resolution function in the Gaussian form with the width of $\Delta(E_e)=0.2468+0.1492\sqrt{E_e}+0.0690E_e$ MeV [@sk08]. The rate of the neutrino event $i$ is evaluated as $$\frac{dN_i}{dt} = \int_{E_{th}}^{\infty} 
\frac{d^2N_i}{dE_e dt} dE_e,$$ where $E_{th}$ is the lowest detectable energy. We suppose a water-[Č]{}erenkov detector of 22.5 kton fiducial volume corresponding to SK detector. We consider 