Traditional search methods primarily depend on string matches, while semantic search targets concept-based matches by recognizing underlying intents and contextual meanings of search terms. Semantic search is particularly beneficial for discovering scholarly publications where differences in vocabulary between users' search terms and document content are common, often yielding irrelevant search results. Many scholarly search engines have adopted knowledge graphs to represent semantic relations between authors, publications, and research concepts. However, users may face challenges when navigating these graphical search interfaces due to the complexity and volume of data, which impedes their ability to discover publications effectively. To address this problem, we developed a conversational search system for exploring scholarly publications using a knowledge graph. We outline the methodical approach for designing and implementing the proposed system, detailing its architecture and functional components. To assess the system's effectiveness, we employed various performance metrics and conducted a human evaluation with 40 participants, demonstrating how the conversational interface compares against a graphical interface with traditional text search. The findings from our evaluation provide practical insights for advancing the design of conversational search systems.