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We use an on-chip superconducting resonator as a sensitive meter to probe the properties of graphene double quantum dots (DQDs) at microwave frequencies. Specifically, we investigate the charge dephasing rates in a circuit quantum electrodynamics (cQED) architecture. The dephasing rates strongly depend on the number of charges in the dots, and the variation has a period of four charges, over an extended range of charge numbers. Although the exact mechanism of this four-fold periodicity in dephasing rates is an open problem, our observations hint at the four-fold degeneracy expected in graphene from its spin and valley degrees of freedom.In recent years, on-chip microwave resonators have emerged as a useful tool both for coupling distant qubits and for sensitive metrology [1]. For example, many experimental studies have recently been performed to study the interaction between quantum dots (QDs) and resonators, in gate-defined carbon-nanotubes [2-4], GaAs [5,6] and InAs nanowire [7,8] structures. Such studies are motivated by considering QDs as promising candidates for quantum information processing. Graphene has also attracted considerable attention in recent years because of its interesting physical properties and potential applications [9]. Like semiconductors, graphene-based QDs have been proposed as potential quantum bits [10]. Various experiments are now underway to study the coherence properties of graphene QDs. For example, using pulsed-gate transient spectroscopy, Volk et al.[11] measured a charge relaxation time of 100 ns in a graphene QD device. However, the dephasing times of grapheme QDs, which benchmark their quantum coherence and may be significantly shorter than their relaxation times, have not yet been measured. In addition, graphene has both spin and valley degrees of freedom, similar to carbon nanotubes [12,13] and Si-based QDs [14]. Spin qubits formed by graphene QDs have been theoretically studied [10], and various valley-related phenomena such as shell filling in carbon nanotubes [12] and valley splitting in silicon [15] have been explored. However, there are no experimental reports on the effects of the four-fold degeneracy caused by the spin and valley degrees in graphene devices.Here, we present an experimental study of a graphene DQD device, which can be considered as a charge qubit that contains a large number of well-defined charge * Corresponding author: gpguo@ustc.edu.cn states. Using the sensitive dispersive readout of a microwave resonator, we measured the charge-state dephasing rates of this DQD in an integrated grapheneresonator device. Applying a quantum model describing the hybrid system, we simultaneously extracted: the DQD-resonator coupling strength, the tunneling rate between each quantum dot, and the charge-state dephasing rates. This microwave spectroscopy overcomes the difficulties of conventional transport techniques and allows us to study DQD dynamics in a large parameter space. In these experiments, we found that the dephasing rates depend on the number of charges in t...