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We combine {\em ab initio} density functional theory (DFT) structural studieswith DFT-based nonequilibrium Green function calculations to investigate howthe presence of non-hexagonal rings affects electronic transport in graphiticstructures. We find that infinite monolayers, finite-width nanoribbons andnanotubes formed of 5-8 haeckelite with only 5- and 8-membered rings aregenerally more conductive than their graphene-based counterparts. Presence ofhaeckelite defect lines in the perfect graphitic structure, a model of grainboundaries in CVD-grown graphene, increases the electronic conductivity andrenders it highly anisotropic.

Electronic Structure and Transport in Graphene/Haeckelite Hybrids: An {\em Ab Initio} Study