Domination in Graph Theory: A Bibliometric Analysis of Research Trends, Collaboration, and Citation Networks

Abstract

This study conducts a comprehensive bibliometric analysis of research on domination in graph theory from 1961 to 2024, based on Scopus-indexed publications retrieved using the query (“dominating” OR “domination”) AND “graph.” The analysis examines publication trends, key contributors, collaboration patterns, citation impact, and emerging research themes. Results indicate a significant and sustained increase in research output, particularly in recent decades. Henning, M.A., Hedetniemi, S.T., and Haynes, T.W. are identified as the most highly cited researchers, underscoring their foundational contributions to the field. Co-authorship network analysis reveals strong international collaborations, with Sheikhholeslami, S.M., exhibiting the highest total link strength, while the United States emerges as the leading hub for global research partnerships. Keyword co-occurrence analysis identifies four major research clusters: graph algorithms, graph-theoretic foundations, domination variants, and binary graph operations. Notably, recent studies increasingly focus on how domination properties evolve under different graph operations. Citation network analysis confirms the enduring influence of foundational studies while highlighting a shift towards computational and applied methodologies. These findings highlight the transition from theoretical to applied research, emphasizing the role of advanced algorithms, interdisciplinary approaches, and large-scale computational techniques. Future research directions should explore machine learning-based optimization, domination in evolving networks, and applications in cybersecurity, bioinformatics, and large-scale social networks.