Graph_Theory_and_Applications_Presentation.pptx
- 1. Graph Theory and Its Applications • An In-depth Overview • Presented by: Srujana • Date: May 4, 2025
- 2. Introduction to Graph Theory • Definition: Graph theory is the study of graphs, mathematical structures to model pairwise relations. • Inventor: Leonhard Euler (1736) • Basic Elements: Vertices (Nodes), Edges (Links) • Types: Directed, Undirected, Weighted, Unweighted
- 3. Basic Terminology • Vertex – a point or node • Edge – a connection between two vertices • Degree – number of edges connected to a vertex • Path – sequence of vertices connected by edges • Cycle – path starting and ending at same vertex • Connected Graph – path exists between all pairs
- 4. Types of Graphs • Simple Graph • Multigraph • Directed Graph (Digraph) • Weighted Graph • Complete Graph • Bipartite Graph • Trees and Forests
- 5. Representation of Graphs • Adjacency Matrix • Adjacency List • Incidence Matrix • (Diagrams not shown here but recommended for final version)
- 6. Key Graph Algorithms • Depth First Search (DFS) • Breadth First Search (BFS) • Dijkstra’s Algorithm (Shortest path) • Prim’s and Kruskal’s Algorithms (MST) • Topological Sorting • Floyd-Warshall Algorithm
- 7. Applications of Graph Theory • Computer Science – Networks, Routing • Biology – DNA sequencing • Social Networks – Influence models • Transport – Route planning • Linguistics – Syntax trees
- 8. Application in Real Life • Google Maps – Shortest path • Facebook – Friend suggestions • Electric Circuits – Represented by graphs • Web Crawling – Pages as nodes and links as edges
- 9. Graph Theory in Artificial Intelligence • Knowledge Graphs • Neural Networks as directed graphs • Game Theory and Decision Trees
- 10. Research Areas • Graph coloring – scheduling • Planar graphs – circuit design • Dynamic graphs – evolving networks • Graph neural networks (GNNs)
- 11. Challenges in Graph Theory • NP-Complete Problems – e.g., Traveling Salesman • Visualization of large graphs • Real-time computation in dynamic graphs
- 12. Conclusion • Graph theory is foundational across fields • Vital for science, engineering, and social sciences • Endless opportunities for exploration
- 13. References • Graph Theory by Reinhard Diestel • Algorithms by Robert Sedgewick • GeeksForGeeks, Khan Academy, etc.