Graph theory is a rapidly evolving and expanding mathematical discipline, with new discoveries, challenges, and techniques emerging every year. Graph Theory: Fundamentals and Applications provides a fully up-to-date and accessible introduction to graph theory, covering both the classical and the modern topics, as well as algorithms and evolving challenges addressed by discipline. Based on the latest syllabi and research trends worldwide, this book includes practical, solved problems that are user friendly to undergraduate, postgraduate, and PhD students, and acts as a key aid in learning the fundamentals and the frontiers of graph theory, as well as developing independent problem-solving and critical thinking skills. This book includes clear instruction in graph representation, basic graph operations, graph connectivity, trees and forests, matching theory, planar graphs and graph drawing, algebraic graph theory, graph traversals, network flows, topological graph theory, and cryptography, among other topics. Each chapter features key term definitions, proofs and algorithms, summary points, and unique exercises to reinforce learning, as well as open problems and research challenges that present unsolved or conjectural problems in graph theory for discussion. Supporting student and instructor sites offer additional exercises, solutions, examples, and case studies in graph theory applications.
1. Introduction to Graph Theory
2. Graph Representation
3. Basic Graph Operations
4. Graph Connectivity
5. Trees and Forests
6. Matching Theory
7. Planar Graphs and Graph Drawing
8. Hamiltonian and Eulerian Graphs
9. Graph Coloring
10. Graph Invariants and Parameters
11. Algebraic Graph Theory
12. Graph Traversals
13. Shortest Path Algorithms
14. Network Flows
15. Topological Graph Theory
16. Ramsey Theory and Extremal Graph Theory
17. Graph Minors and Decompositions
18. Graph Algorithms and Complexity Theory
19. Graphs and Cryptography
20. Graphs and Machine Learning
21. Random Graphs and Probabilistic Methods
22. Research Challenges and Open Problems
23. Appendices
Sovan Samanta is an assistant professor in the Department of Mathematics, Tamralipta Mahavidyalaya, India and scientific advisor of Algebra Bernays University, Gradiscanska, Zagreb, Croatia. He is also a Visiting Professor at Instiya University, Turkey. Before that, he worked as an Assistant Professor in the Department of Basic Sciences at the Indian Institute of Information Technology, Nagpur. He holds a PhD in algebraic fuzzy graph theory from Vidyasagar University, India and a Post Doc in discrete mathematics from Hanyang University, South Korea. He has published over 87 papers in international journals, including 65 in SCIE/SCI journals. He has also authored and edited several books and book chapters, and serves as an Associate Editor for the Journal of Applied Mathematics and Computing, the Journal of Intelligent & Fuzzy Systems, and Mathematical Problems in Engineering. Kinkar Chandra Das is a Professor in the Department of Mathematics at Sungkyunkwan University. He received his M.Tech. degree in Computer Science and Data Processing and his Ph.D. in Spectral Graph Theory from the Indian Institute of Technology, Kharagpur, in 2004. He was awarded a prestigious French scholarship by the Ministry of France, which allowed him to spend a year at LRI, University of Paris XI. His primary research interests include spectral graph theory, algebraic graph theory, molecular graph theory, degree sequences of graphs, and graph coloring. He has published more than 387 research papers in leading international journals. He has also authored several books published by Springer and other reputable international publishers. Professor Das has served as an associate editor and editorial board member for various SCI(E)-indexed international journals, including MATCH Communications in Mathematical and in Computer Chemistry and the Journal of Applied Mathematics and Computing, etc. He has undertaken numerous research fellowships, academic visits, and conference engagements across 25 countries worldwide. He is the recipient of several notable awards, including the Sungkyunkwan Family Award 2014” and the SKKU Young Fellowship 2019. He also received the University Gold-Centered Silver Medal for securing first place in his undergraduate studies.
