  The multiplicity and pseudorapidity distributions of inclusive photons have
been measured at forward rapidities ($2.3 < \eta < 3.9$) in proton-proton
collisions at three center-of-mass energies, $\sqrt{s}=0.9$, 2.76 and 7 TeV
using the ALICE detector. It is observed that the increase in the average
photon multiplicity as a function of beam energy is compatible with both a
logarithmic and a power-law dependence. The relative increase in average photon
multiplicity produced in inelastic pp collisions at 2.76 and 7 TeV
center-of-mass energies with respect to 0.9 TeV are 37.2% $\pm$ 0.3% (stat)
$\pm$ 8.8% (sys) and 61.2% $\pm$ 0.3% (stat) $\pm$ 7.6% (sys), respectively.
The photon multiplicity distributions for all center-of-mass energies are well
described by negative binomial distributions. The multiplicity distributions
are also presented in terms of KNO variables. The results are compared to model
predictions, which are found in general to underestimate the data at large
photon multiplicities, in particular at the highest center-of-mass energy.
Limiting fragmentation behavior of photons has been explored with the data, but
is not observed in the measured pseudorapidity range.
