  Future large liquid-scintillator detectors can be implemented to observe
neutrinos from a core-collapse supernova (SN) in our galaxy in various reaction
channels: (1) The inverse beta decay $\overline{\nu}^{}_e + p \to n + e^+$; (2)
The elastic neutrino-proton scattering $\nu + p \to \nu + p$; (3) The elastic
neutrino-electron scattering $\nu + e^- \to \nu + e^-$; (4) The charged-current
$\nu^{}_e$ interaction $\nu^{}_e + {^{12}}{\rm C} \to e^- + {^{12}}{\rm N}$;
(5) The charged-current $\overline{\nu}^{}_e$ interaction $\overline{\nu}^{}_e
+ {^{12}}{\rm C} \to e^+ + {^{12}}{\rm B}$; (6) The neutral-current interaction
$\nu + {^{12}}{\rm C} \to \nu + {^{12}}{\rm C}^*$. The less abundant $^{13}{\rm
C}$ atoms in the liquid scintillator are also considered as a target, and both
the charged-current interaction $\nu^{}_e + {^{13}}{\rm C} \to e^- +
{^{13}}{\rm N}$ and the neutral-current interaction $\nu + {^{13}}{\rm C} \to
\nu + {^{13}}{\rm C}^*$ are taken into account. In this work, we show for the
first time that a global analysis of all these channels at a single
{liquid-}scintillator detector, such as Jiangmen Underground Neutrino
Observatory (JUNO), is very important to test the average-energy hierarchy of
SN neutrinos and how the total energy is partitioned among neutrino flavors. In
addition, the dominant channels for reconstructing neutrino spectra and the
impact of other channels are discussed in great detail.
