Vertex-Based Labeling Games

This book provides a concise introduction to graph labeling games, an area at the intersection of graph theory and combinatorial game theory. It presents the fundamental concepts, techniques, and recent developments of the field while highlighting connections with classical graph labeling methods. By bringing together key results and perspectives within a unified framework, the book offers readers an accessible entry point to this growing research area. Covering both established and emerging graph labeling games, the book examines topics such as the graceful game, the range-relaxed graceful game, Edge-Sum Distinguishing labeling games, and other games based on sums and differences of labels. Classical graph families and graph products are used to illustrate key ideas, while winning strategies, bounds, and shared mathematical techniques are developed across different labeling schemes. Each chapter combines definitions, results, open problems, and exercises, encouraging readers to engage with current challenges and future research directions. Written for graduate students and researchers in graph theory, discrete mathematics, combinatorial game theory, and theoretical computer science, this volume serves as a research-oriented reference on graph labeling games. By consolidating current knowledge and identifying directions for future work, it equips readers with the tools and insights needed to pursue research in this evolving field.