  A search is conducted for new physics in final states containing a photon and
missing transverse momentum in proton-proton collisions at $\sqrt{s} =$ 13 TeV,
using the data collected in 2016 by the CMS experiment at the LHC,
corresponding to an integrated luminosity of 35.9 fb$^{-1}$. No deviations from
the predictions of the standard model are observed. The results are interpreted
in the context of dark matter production and models containing extra spatial
dimensions, and limits on new physics parameters are calculated at 95%
confidence level. For the two simplified dark matter production models
considered, the observed (expected) lower limits on the mediator masses are
both 950 (1150) GeV for 1 GeV dark matter mass. For an effective
electroweak-dark matter contact interaction, the observed (expected) lower
limit on the suppression parameter $\Lambda$ is 850 (950) GeV. Values of the
effective Planck scale up to 2.85-2.90 TeV are excluded for between 3 and 6
extra spatial dimensions.
