  The spectrum and amplitude of the stochastic background of relic gravitons
produced in a bouncing universe is calculated. The matter content of the model
consists of dust and radiation fluids, and the bounce occurs due to quantum
cosmological effects when the universe approaches the classical singularity in
the contracting phase. The resulting amplitude is very small and it cannot be
observed by any present and near future gravitational wave detector. Hence, as
in the ekpyrotic model, any observation of these relic gravitons will rule out
this type of quantum cosmological bouncing model.
