The frequent exchange of multimedia information in the present era projects an increasing demand for copyright protection. In this work, we propose a novel audio zero-watermarking technology based on graph Fourier transform for enhancing the robustness with respect to copyright protection. In this approach, the combined shift operator is used to construct the graph signal, upon which the graph Fourier analysis is performed. The selected maximum absolute graph Fourier coefficients representing the characteristics of the audio segment are then encoded into a feature binary sequence using K-means algorithm. Finally, the resultant feature binary sequence is XOR-ed with the watermark binary sequence to realize the embedding of the zero-watermarking. The experimental studies show that the proposed approach performs more effectively in resisting common or synchronization attacks than the existing state-of-the-art methods.