Text classification is a fundamental problem in information retrieval with many real-world applications, such as predicting the topics of online articles and the categories of e-commerce product descriptions. However, low-resource text classification, with no or few labeled samples, presents a serious concern for supervised learning. Meanwhile, many text data are inherently grounded on a network structure, such as a hyperlink/citation network for online articles, and a user-item purchase network for e-commerce products. These graph structures capture rich semantic relationships, which can potentially augment low-resource text classification. In this paper, we propose a novel model called Graph-Grounded Pre-training and Prompting (G2P2) to address low-resource text classification in a two-pronged approach. During pre-training, we propose three graph interaction-based contrastive strategies to jointly pre-train a graph-text model; during downstream classification, we explore handcrafted discrete prompts and continuous prompt tuning for the jointly pre-trained model to achieve zero- and few-shot classification, respectively. Moreover, we explore the possibility of employing continuous prompt tuning for zero-shot inference. Specifically, we aim to generalize continuous prompts to unseen classes while leveraging a set of base classes. To this end, we extend G2P2 into G2P2$^*$, hinging on a new architecture of conditional prompt tuning. Extensive experiments on four real-world datasets demonstrate the strength of G2P2 in zero- and few-shot low-resource text classification tasks, and illustrate the advantage of G2P2$^*$ in dealing with unseen classes.