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Deriving mathematical expressions of two zero modes for a $\pi$-bandtight-binding model, we identify a class of bipartite graphs having the samenumber of subgraph sites, where each graph represents one of thequasi-hexagonal nanographene molecule with a center vacancy (VANG). Indeed, ina VANG molecule, C$_{60}$H$_{24}$, showing stability in a density-functionalsimulation at the highest occupied level, there appear two pseudo-degeneratezero modes, a vacancy-centered quasi-localized zero mode, and extending zeromode with a $\sqrt{3} \times \sqrt{3}$ structure. Since there is a finiteenergy gap between these two zero-energy modes and the other modes, low-lyingstates composed of quasi-degenerate zero modes appear as magnetic multiplets.Thus, the unique magnetic characteristics derived in our theory are expected tohold for synthesized VANG molecules in reality.

Theoretical Analysis on Pseudo-Degenerate Zero-Energy Modes in Vacancy-Centered Hexagonal Armchair Nanographene