In the era of widespread social networks, the rapid dissemination of fake news has emerged as a significant threat, inflicting detrimental consequences across various dimensions of people's lives. Machine learning and deep learning approaches have been extensively employed for identifying fake news. However, a significant challenge in identifying fake news is the limited availability of labeled news datasets. Therefore, the One-Class Learning (OCL) approach, utilizing only a small set of labeled data from the interest class, can be a suitable approach to address this challenge. On the other hand, representing data as a graph enables access to diverse content and structural information, and label propagation methods on graphs can be effective in predicting node labels. In this paper, we adopt a graph-based model for data representation and introduce a semi-supervised and one-class approach for fake news detection, called LOSS-GAT. Initially, we employ a two-step label propagation algorithm, utilizing Graph Neural Networks (GNNs) as an initial classifier to categorize news into two groups: interest (fake) and non-interest (real). Subsequently, we enhance the graph structure using structural augmentation techniques. Ultimately, we predict the final labels for all unlabeled data using a GNN that induces randomness within the local neighborhood of nodes through the aggregation function. We evaluate our proposed method on five common datasets and compare the results against a set of baseline models, including both OCL and binary labeled models. The results demonstrate that LOSS-GAT achieves a notable improvement, surpassing 10%, with the advantage of utilizing only a limited set of labeled fake news. Noteworthy, LOSS-GAT even outperforms binary labeled models.