  We present a theoretical study of the structural and electronic properties of
graphene monolayer functionalized with boron and nitrogen atoms substituting
carbon atoms. Our study is based on the ab initio calculations in the framework
of the density functional theory. We calculate the binding energies of the
functionalized systems, changes in the morphology caused by functionalization,
and further the band gap energy as a function of the concentration of dopants.
Moreover, we address the problem of possible clustering of dopants at a given
concentration. We define the clustering parameter to quantify the dependence of
the properties of the functionalized systems on the distribution of B/N atoms.
  We show that clustering of B/N atoms in graphene is energetically unfavorable
in comparison to the homogenous distribution of dopants. For most of the
structures, we observe a nonzero energy gap that is only slightly dependent on
the concentration of the substituent atoms.
