Exploratory search is an open-ended information retrieval process that aims at discovering knowledge about a topic or domain rather than searching for a specific answer or piece of information. Conversational interfaces are particularly suitable for supporting exploratory search, allowing users to refine queries and examine search results through interactive dialogues. In addition to conversational search interfaces, knowledge graphs are also useful in supporting information exploration due to their rich semantic representation of data items. In this study, we demonstrate the synergistic effects of combining knowledge graphs and conversational interfaces for exploratory search, bridging the gap between structured and unstructured information retrieval. To this end, we propose a knowledge-driven dialogue system for exploring news articles by asking natural language questions and using the graph structure to navigate between related topics. Based on a user study with 54 participants, we empirically evaluate the effectiveness of the graph-based exploratory search and discuss design implications for developing such systems.