  We present an exactly solvable toy model for the continuous dissipative
dynamics of permutation-invariant graph states of $N$ qubits. Such states are
locally equivalent to an $N$-qubit Greenberger-Horne-Zeilinger (GHZ) state, a
fundamental resource in many quantum information processing setups. We focus on
the time evolution of the state governed by a Lindblad master equation with the
three standard single-qubit jump operators, the Hamiltonian part being set to
zero. Deriving analytic expressions for the expectation values of observables
expanded in the Pauli basis at all times, we analyze the nontrivial
intermediate-time dynamics. Using a numerical solver based on matrix product
operators, we simulate the time evolution for systems with up to 64 qubits and
verify a numerically exact agreement with the analytical results. We find that
the evolution of the operator space entanglement entropy of a bipartition of
the system manifests a plateau whose duration increases logarithmically with
the number of qubits, whereas all Pauli-operator products have expectation
values decaying at most in constant time.
