Non-equilibrium molecular dynamics is used to investigate the heat current
due to the atomic lattice vibrations in graphene nanoribbons and nanorings
under a thermal gradient. We consider a wide range of temperature, nanoribbon
widths up to 6nm and the effect of moderate edge disorder. We find that narrow
graphene nanorings can efficiently suppress the lattice thermal conductivity at
low temperatures (~100K), as compared to nanoribbons of the same width.
Remarkably, rough edges do not appear to have a large impact on lattice energy
transport through graphene nanorings while nanoribbons seem more affected by
imperfections. Furthermore, we demonstrate that the effects of
hydrogen-saturated edges can be neglected in these graphene nanostructures
