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We consider the Dirac equation on periodic networks (quantum graphs). Theself-adjoint quasi periodic boundary conditions are derived. The secularequation allowing us to find the energy spectrum of the Dirac particles onperiodic quantum graphs is obtained. Band spectra of the periodic quantumgraphs of different topologies are calculated. Universality of the probabilityto be in the spectrum for certain graph topologies is observed.

Dirac particles on periodic quantum graphs