Rumors in different topic domains have different text characteristics but similar emotional tendencies. To resolve the scarce-data problem in some rumor-topic domains, this study proposes a cross-domain rumor-propagation model, which is based on transfer learning. First, given the diversity and complexity of the rumor-propagation landscape, this study introduces a novel method, User-Retweet-Rumor2vec (URR2vec), which leverages the power of representation learning to uncover latent features within rumor topics. It also displays the forwarding relationship between users and rumors, user node information, and rumor-topic information in low-dimensional space. To capture the impact of human emotional cognition during rumor spreading, we also introduce a deep-learning model based on the natural language texts of rumor topics, which analyzes the sentiment in the text and uncovers the emotional correlations among users. Furthermore, a rumor-propagation prediction model based on the text-sentiment analysis-graph convolutional network (TSA-GCN) is proposed and pre-trained on existing rumor-topic data to ensure its prediction accuracy. Finally, considering the data sparsity at a rumor-topic outbreak, the trained propagation model is transferred to the rumor topic for prediction. Meanwhile, the rumor topic in different domains has different edges and conditional distribution, similar emotional characteristics, and network structure among the rumor topics. After fine-tuning the parameter and adding a domain adaptation layer in TSA-GCN, a domain adaptation model based on parameter and graph-structure migration is obtained.