Graphullerene, an emerging class of two-dimensional (2D) carbon allotropes constructed by covalently interlinked fullerene molecules, holds great promise for electronics, photocatalysis, and energy storages. Using first-principles calculations, we design three stable graphullerene monolayers based on the smallest fullerene ${\mathrm{C}}_{20}$—quasitetragonal GrF1-${\mathrm{C}}_{20}$ and GrF2-${\mathrm{C}}_{20}$, along with quasihexagonal LOPC-${\mathrm{C}}_{20}$. Their successful stabilization provides a valuable reference for understanding the formation mechanisms of fullerene-based networks. Unlike large-band-gap ${\mathrm{C}}_{60}$-based graphullerenes, these ${\mathrm{C}}_{20}$ systems exhibit widely tunable electronic properties dictated by their bonding patterns: GrF1-${\mathrm{C}}_{20}$ possesses an ultranarrow band gap, while GrF2-${\mathrm{C}}_{20}$ and LOPC-${\mathrm{C}}_{20}$ are wide-gap semiconductors. Remarkably, GrF2-${\mathrm{C}}_{20}$ demonstrates suitable band edge alignment for photocatalytic overall water splitting under neutral conditions. The most striking finding is the strain-induced magnetic transition in GrF1-${\mathrm{C}}_{20}$. Compressive strain polarizes the unpaired ${\mathrm{p}}_{\mathrm{z}}$ electrons, mediating the emergence of magnetism. At a critical uniaxial strain of ∼4%, the system transitions into a half-metallic state. Furthermore, the band gap magnitude and direct/indirect nature of LOPC-${\mathrm{C}}_{20}$ are highly susceptible to mechanical strain. Our work not only pioneers the exploration of ${\mathrm{C}}_{20}$-based graphullerenes but also highlights strain engineering as a powerful tool for tailoring their electronic and magnetic properties, offering key design strategies for future carbon-based optoelectronic and spintronic devices.

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• Density of states
• Electronic structure
• Magnetic anisotropy
• Molecular magnetism
• Spintronics
• Stress
• First-principles calculations