  In this work we consider a model for particle dark matter where an extra
inert Higgs doublet and an additional scalar singlet is added to the Standard
Model (SM) Lagrangian. The dark matter candidate is obtained from only the
inert doublet. The stability of this one component dark matter is ensured by
imposing a $Z_2$ symmetry on this additional inert doublet. The additional
singlet scalar has a vacuum expectation value (VEV) and mixes with the Standard
Model Higgs doublet resulting in two CP even scalars $h_1$ and $h_2$. We treat
one of these scalars, $h_1$, to be consistent with the SM Higgs like boson of
mass around 125 GeV reported by the LHC experiment. These two CP even scalars
affect the annihilation cross-section of this inert doublet dark matter
resulting in a larger dark matter mass region that satisfies the observed relic
density. We also investigate the $h_1 \rightarrow \gamma\gamma$ and $h_1
\rightarrow \gamma Z$ processes and compared these with LHC results. This is
also used to constrain the dark matter parameter space in the present model. We
find that the dark matter candidate in the mass region $\frac {m_1} {2} < m_H <
m_W$ GeV ($m_1 = 125$ GeV, mass of $h_1$) satisfies the recent bound from LUX
direct detection experiment.
