Parasupersymmetry in quantum graphs

We study hidden parasupersymmetry structures in purely bosonic quantum mechanics on compact equilateral graphs. We consider a single free spinless particle on the graphs and show that the Huang–Su parasupersymmetry algebra is hidden behind degenerate spectra.

► Parasupersymmetry is hidden behind degenerate spectra in equilateral quantum graphs.
► ZNZN cyclic symmetry transformation on the graphs plays the role of grading operator.
► We classified parasupersymmetry invariant boundary conditions.
► Cheon’s spiral holonomy appears along with spontaneous parasupersymmetry breaking.