  Carbon based two-dimensional (2D) materials with honeycomb lattices, like
graphene, polyaniline carbon-nitride (C$_3$N) and boron-carbide (BC$_3$)
exhibit exceptional physical properties. On this basis, we propose two novel
graphene-like materials with BC$_6$N stoichiometry. We conducted
first-principles calculations to explore the stability, mechanical response,
electronic, optical and thermal transport characteristics of graphene-like
BC$_3$ and BC$_6$N monolayers. The absence of imaginary frequencies in the
phonon dispersions confirm dynamical stability of BC$_3$ and BC$_6$N
monolayers. Our first principles results reveal that BC$_3$ and BC$_6$N present
high elastic moduli of 256 and 305 N/m, and tensile strengths of 29.0 and 33.4
N/m, with room temperature lattice thermal conductivities of 410 and 1710
W/m.K, respectively. Notably, the thermal conductivity of BC$_6$N is one of the
highest among all 2D materials. According to electronic structure calculations,
monolayers of BC$_3$ and BC$_6$N are indirect and direct bandgap
semiconductors, respectively. The optical analysis illustrate that the first
absorption peaks along the in-plane polarization for single-layer BC$_3$ and
BC$_6$N occur in the visible range of the electromagnetic spectrum. Our results
reveal outstandingly high mechanical properties and thermal conductivity along
with attractive electronic and optical features of BC$_3$ and BC$_6$N
nanosheets and present them as promising candidates to design novel
nanodevices.
