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Geometric graph model is suggested for the dynamical Casimir effect. The wave equation is considered at the graph edges and the Kirchhoff condition at the internal vertex. It is assumed that the edge lengths depend on time. Photon generation is considered in the framework of the Dodonov–Klimov model.

Quantum graphs with varying edges lengths are constructed. We deal with two types of operators on the graph edges: the Schrodinger and the Dirac operators. The dynamics of quantum particles for these two cases is compared. From the physical point of view, the Schrodinger dynamics corresponds to nonrelativistic particle and the Dirac dynamics to the relativistic one.