Speaker verification systems face threat from various spoofing attacks and particularly, the physical access attacks or replay attacks that are most common show an imminent threat. Literature shows that graph signal processing (GSP) shows a better correlation between speech samples and explore more hidden information from speech than the traditional digital signal processing methods. With this motivation, we propose a novel feature based on GSP, namely, graph frequency cepstral coefficient (GFCC). We use the combined shift operator to construct the graph signal, and then carry out the graph Fourier analysis to extract GFCC features. It is observed that compared to fast Fourier transform, the GFT can more accurately represent the structural relationship of speech samples, which makes the real and replay speech very distinguishable in the frequency domain. We use the GFCC features with a light convolutional neural network system in our studies. The results on ASVspoof 2019 physical access corpus show that the proposed GFCC feature based system outperforms the challenge baselines by a large margin and emerge as one of the best performing state-of-the-art single systems.