  Massive cosmological neutrinos suppress the Large-Scale Structure (LSS) in
the Universe by smoothing the cosmic over-densities, and hence structure
formation is delayed relative to that in the standard Lambda-Cold Dark Matter
($\Lambda$CDM) model. We characterize the merger and mass accretion history of
dark matter halos with the halo formation time $a_{1/2}$, tree entropy $s$ and
halo leaf function $\ell(X)$ and measure them using neutrino-involved N-body
simulations. We show that a non-zero sum of neutrino masses $M_\nu$ delays the
$a_{1/2}$ for halos with virial mass between $10^{13} M_\odot$ and $3\times
10^{13} M_\odot$, whereas a non-zero neutrino asymmetry parameter $\eta^2$ has
the opposite effect. While the mean tree entropy $\bar s$ does not depend
significantly on either $M_\nu$ or $\eta^2$, the halo leaf function does.
Furthermore, the dependencies of $\ell$ on $M_\nu$ and $\eta^2$ have
significant evolution in redshift $z$, with the relative contributions of
$M_\nu$ and $\eta^2$ showing a sigmoid-like transition as a function of $z$
around $z \approx 0.6$. Together with the matter power spectrum, these halo
parameters allow us to break the parameter degeneracy between $M_\nu$ and
$\eta^2$ so that they can both be constrained in principle.
