  We present density functional theory calculations of the binding energies of
one, two and three fluorine adatoms on the same side of monolayer graphene. We
show that fluorine dimers on graphene in a spin-singlet state are stable
against dissociation into isolated fluorine adatoms, suggesting that there is a
tendency for fluorine adatoms on a single side of graphene to cluster. Our
results suggest that fluorination develops by successive bonding of fluorine
atoms to neighbouring carbon atoms on different sublattices, while the spins
are arranged to reduce the total magnetisation of the ground state. We find
that the finite-size error in the binding energy of a single fluorine atom or
dimer on a periodic supercell of graphene scales inversely with the cube of the
linear size of the simulation supercell. By using $\pi$-orbital axis analysis,
the rehybridisation of the three $\sigma$-orbitals pointing directly along the
bonds to the central fluorinated carbon is found to be
sp\textsuperscript{2.33}. The rehybridisation of the carbon orbital in the C--F
bond is found to be sp\textsuperscript{4.66}.
