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.

Simone Dantas is a Full Professor at the Institute of Mathematics and Statistics of Fluminense Federal University (UFF), Brazil, where she founded the research area of Discrete Mathematics and Combinatorics within the Graduate Program in Mathematics. She holds a PhD in Systems Engineering and Computer Science from the Federal University of Rio de Janeiro (UFRJ), including a doctoral research period at Université Joseph Fourier, and completed postdoctoral research at Brown University and the University of Campinas (UNICAMP). Her research interests include discrete mathematics, combinatorics, graph theory, and theoretical computer science. She is a CNPq Research Productivity Fellow (Level A).

Atílio G. Luiz is an Associate Professor at the Federal University of Ceará (UFC), Quixadá Campus, Brazil, and a member of the Graduate Program in Computing (PCOMP). He received his PhD and MSc in Computer Science from the University of Campinas (UNICAMP), including research periods at the University of Waterloo, Canada, during both his doctoral and master's studies. His research focuses on combinatorics, graph theory, and algorithms, with particular interests in graph coloring, domination, and graph labeling.

Deise L. de Oliveira is a Professor at the Federal Institute of Rio de Janeiro (IFRJ), Brazil. She earned her PhD in Mathematics from the Fluminense Federal University (UFF), where her doctoral thesis received an Honorable Mention in the Brazilian Society of Applied and Computational Mathematics (SBMAC) Thesis Award. Her research interests include discrete mathematics and combinatorics, particularly graph labeling games, as well as mathematical modeling, linear algebra, and mathematics education.