Graph theory combinatorics and algorithms interdisciplinary applications 1st Edition by Martin Charles Golumbic, Irith Ben Arroyo Hartman ISBN 9780387250366 0387250360

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Product details:
ISBN 10: 0387250360
ISBN 13: 9780387250366
Author: Martin Charles Golumbic, Irith Ben Arroyo Hartman
 

Graph theory combinatorics and algorithms interdisciplinary applications 1st Edition Table of contents:

Part I: Basic Graph Theory and Combinatorics

2. Fundamentals of Graph Theory

   • Definitions: Graphs, Vertices, and Edges
   • Types of Graphs: Directed, Undirected, Bipartite
   • Paths, Cycles, and Connectivity
   • Graph Traversal Algorithms: DFS and BFS

3. Basic Combinatorial Structures

   • Permutations and Combinations
   • Counting Principles in Combinatorics
   • Pigeonhole Principle and Inclusion-Exclusion
   • Binomial Coefficients and Their Applications

4. Trees and Forests

   • Definitions and Properties of Trees
   • Tree Traversals: Preorder, Inorder, Postorder
   • Spanning Trees and Minimum Spanning Trees
   • Applications of Trees in Algorithms

Part II: Advanced Topics in Graph Theory

5. Planar Graphs and Graph Coloring

   • Definitions and Properties of Planar Graphs
   • Euler’s Formula and the Four Color Theorem
   • Graph Coloring Algorithms
   • Applications in Scheduling and Map Coloring

6. Network Flows and Matching Theory

   • Flow Networks and Max-Flow Min-Cut Theorem
   • Algorithms for Computing Maximum Flow
   • Bipartite Graph Matching
   • Applications in Network Design and Resource Allocation

7. Graph Algorithms and Computational Complexity

   • Time Complexity and Asymptotic Notation
   • Polynomial-Time Algorithms and NP-Completeness
   • Approximation Algorithms for Graph Problems
   • Hardness Results in Graph Theory

8. Random Graphs and Probabilistic Methods

   • Erdős-Rényi Model and Random Graphs
   • Probabilistic Techniques in Graph Theory
   • Applications of Random Graphs in Computer Science and Biology
   • Percolation Theory and Random Walks

Part III: Combinatorics in Algorithms and Applications

9. Combinatorial Optimization

   • Basic Optimization Problems and Techniques
   • Linear Programming and Integer Programming
   • Greedy Algorithms for Combinatorial Problems
   • Dynamic Programming and Backtracking Approaches

10. Combinatorics in Coding Theory

    • Error-Correcting Codes and Their Applications
    • The Hamming Distance and Code Performance
    • Graph-Based Codes and Their Use in Communication Systems
    • Algorithms for Code Construction and Decoding

11. Design Theory and Block Designs

    • Introduction to Design Theory
    • Block Designs and Their Combinatorial Properties
    • Applications in Experimental Design and Coding Theory
    • Algorithms for Constructing Block Designs

Part IV: Interdisciplinary Applications

12. Graph Theory and Operations Research

    • Graphs in Optimization and Decision-Making
    • Network Design, Flow Problems, and Logistics
    • Algorithms for Transportation and Supply Chain Management
    • Applications in Manufacturing and Resource Scheduling

13. Graph Theory in Computer Networks and Distributed Systems

    • Topology of Computer Networks
    • Routing Algorithms and Network Flow
    • Distributed Algorithms for Multi-Agent Systems
    • Applications in Cloud Computing and Peer-to-Peer Networks

14. Combinatorics in Biology and Bioinformatics

    • Graph Models for Biological Networks
    • Algorithms for Gene Sequencing and Protein Folding
    • Combinatorial Problems in Evolutionary Biology
    • Applications in Computational Biology and Systems Biology

15. Graph Theory in Social Networks and Data Mining

    • Social Network Analysis and Graph Theory
    • Community Detection and Influence Propagation
    • Graph-Based Data Mining Algorithms
    • Applications in Marketing, Politics, and Sociology

Conclusion
16. Future Directions in Graph Theory and Combinatorics
– Emerging Trends in Graph Algorithms
– The Role of Graph Theory in AI and Machine Learning
– New Applications and Interdisciplinary Research Areas
– Final Thoughts on the Future of Graph Theory and Combinatorics

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