  We study the vacuum stability and unitarity conditions for a 125 GeV Standard
Model (SM)-like Higgs boson mass in the type-II seesaw model. We find that, as
long as the seesaw scale is introduced below the SM vacuum instability bound,
there exists a large parameter space predicting a 125 GeV Higgs mass,
irrespective of the exact value of the seesaw scale, satisfying both stability
and unitarity conditions up to the Planck scale. We also study the model
predictions for the Higgs partial decay widths in the diphoton and Z+photon
channels with respect to their SM expectations and find that the decay rates
for these two processes are correlated. We further show that for any given
enhancement in the Higgs-to-diphoton rate over its SM expectation, there exists
an upper bound on the type-II seesaw scale, and hence, on the masses of the
associated doubly- and singly-charged Higgs bosons in the allowed parameter
space. For instance, if more than 10% enhancement persists in the
Higgs-to-diphoton channel, the upper limit on the type-II seesaw scale is about
450 GeV which is completely within the reach of the 14 TeV LHC. We believe this
to be an encouraging result for the experimental searches of the singly- and
doubly-charged Higgs bosons which, in combination with improved sensitivity in
the Higgs-to-diphoton and Higgs-to-Z+photon signal strengths, could probe the
entire allowed parameter space of the minimal type-II seesaw model, and
establish/eliminate it as a single viable extension of the SM.
