A new graph theory to unravel the bulk-boundary correspondence of graphene nanoribbons

We developed a new graph theory rooted in Clar's sextet rule to unravel the bulk-boundary correspondence of graphene. This methodology is specifically focused on the topological invariant and the chiral winding number, which enables the chemical rationalization of edge and boundary states in one-dimensional graphene nanoribbon (GNR) materials. The Clar structure derived from facile Lewis structures facilitates direct prediction of free radical distribution along edges and boundaries of GNRs across various geometric configurations. We then extend this graph theoretical framework to include metallic GNRs, demonstrating its power in several paradigms where conventional topological theories show limitations. Upon reducing the topological parameters and hence the complexity, the new approach provides a visual comprehension for the electronic topology and hence conductivity of GNR, greatly simplifying the formulation of design principles for future application of graphene interconnects.