Topologically protected Majorana zero modes (MZMs) have attracted intense interest due to their potential application in fault-tolerant quantum computation (TQC). Graphene nanoribbons, with tunable edge terminations and compatibility with planar device architectures, offer a promising alternative to semiconductor nanowires. Here we present a comprehensive theoretical study of finite graphene strips with armchair, zigzag, and nearly square geometries, proximitized by an s-wave superconductor and subject to Rashba spin-orbit coupling, Zeeman fields, and disorder. Using exact diagonalization of the Bogoliubov-de Gennes tight-binding Hamiltonian, we analyze Majorana polarization, a Pfaffian-based periodic-disorder topological indicator (PDI), low-energy spectra, and real-space wavefunctions to identify the nontrivial topological phases supporting MZMs and distinguish them from partially separated Andreev bound states (psABS) or quasi-Majoranas. We systematically chart the robustness of these modes across geometries and disorder regimes, finding that armchair strips with short zigzag edges provide the most stable platform. Our results unify polarization and PDI diagnostics with spatial wavefunction analysis and disorder effects, yielding concrete design guidelines for graphene-based topological superconductors.

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• Andreev bound states
• Edge states
• Localization
• Majorana bound states
• Majorana fermions
• Order parameters
• Phase diagrams
• Quantum phase transitions
• Quasiparticles & collective excitations
• Spin-orbit coupling
• Topological superconductors
• Graphene
• Topological materials
• Exact diagonalization
• Symmetries in condensed matter
• Tight-binding model