1. Graph Basics
·      Representing Graphs Using Adjacency Matrix
·      Representing Graphs Using Adjacency List
·      Implementing a Graph Using an Edge List
·      Implementing Depth-First Search (DFS)
·      Implementing Breadth-First Search (BFS)
·      Checking if a Graph is Connected (Undirected)
·      Counting Connected Components in an Undirected Graph
·      Checking if a Graph is Bipartite (DFS and BFS)
·      Detecting Cycle in an Undirected Graph (DFS and BFS)
·      Detecting Cycle in a Directed Graph (DFS and BFS)
 
 2. Shortest Path Algorithms
·      Dijkstra’s Algorithm
·      Bellman-Ford Algorithm
·      Floyd-Warshall Algorithm
·      Shortest Path in a Grid (BFS)
·      Shortest Path in a Weighted Graph (Using Priority Queue)
·      0-1 BFS for Shortest Path in a Binary Graph
·      Shortest Path in a Directed Acyclic Graph (DAG)
·      Shortest Path in a Grid with Obstacles
·      Shortest Path with Exactly K Edges
·      All Pairs Shortest Path (Floyd-Warshall)
 
 3. Graph Traversal and Connected Components
·      Connected Components in an Undirected Graph
·      Connected Components in a Directed Graph (Kosaraju’s Algorithm)
·      Strongly Connected Components (Tarjan’s Algorithm)
·      Articulation Points (Cut Vertices) in a Graph
·      Bridges in a Graph
·      Biconnected Components
·      Finding All Cycles in a Graph
·      Counting Cycles of Length 3 in an Undirected Graph
·      Counting Cycles of Length 4 in an Undirected Graph
·      Eulerian Path and Circuit in an Undirected Graph
 
 4. Topological Sorting and DAGs
·      Topological Sorting Using DFS
·      Topological Sorting Using Kahn’s Algorithm (BFS)
·      Longest Path in a Directed Acyclic Graph (DAG)
·      Finding All Topological Orderings of a DAG
·      Critical Path Method (CPM)
·      Detecting Cycle in a DAG
·      Minimum Number of Vertices to Traverse All Nodes (DAG)
·      Path with Maximum Probability in a Directed Graph
·      Kahn’s Algorithm for Detecting Cycles in a Graph
·      Converting a Directed Graph to a DAG (Removing Cycles)
 
 5. Minimum Spanning Tree (MST) Algorithms
·      Prim’s Algorithm
·      Kruskal’s Algorithm
·      Minimum Spanning Tree for a Graph with Negative Weights
·      Finding Second Minimum Spanning Tree
·      Checking Uniqueness of Minimum Spanning Tree
·      Boruvka’s Algorithm for MST
·      Finding the Maximum Spanning Tree
·      Minimum Cost to Connect All Points (Using MST)
·      Minimum Spanning Tree for Dense Graphs
·      Minimum Spanning Tree in a Grid
 
 6. Network Flow and Matching Problems
·      Ford-Fulkerson Algorithm for Maximum Flow
·      Edmonds-Karp Algorithm for Maximum Flow
·      Dinic’s Algorithm for Maximum Flow
·      Minimum Cut in a Graph (Max-Flow Min-Cut Theorem)
·      Bipartite Matching Using Network Flow
·      Maximum Bipartite Matching (Hungarian Algorithm)
·      Minimum Vertex Cover in a Bipartite Graph
·      Finding Disjoint Paths in a Graph
·      Circulation Problem in a Network
·      Job Assignment Problem (Hungarian Algorithm)
 
 7. Graph Coloring Problems
·      Graph Coloring Using Backtracking
·      Minimum Colors Required to Color a Graph (Greedy)
·      Chromatic Number of a Graph
·      Coloring a Bipartite Graph
·      M-Coloring Problem (Backtracking)
·      Vertex Coloring in a Tree
·      Edge Coloring of a Graph
·      Planar Graph Coloring (Four-Color Theorem)
·      Graph Coloring to Solve Sudoku
·      Coloring Graphs to Solve Map Coloring Problem
 
 8. Advanced Graph Algorithms
·      Johnson’s Algorithm for All-Pairs Shortest Path
·      A* Search Algorithm
·      Bidirectional Search Algorithm
·      Tarjan’s Algorithm for Bridge-Finding
·      Floyd-Warshall with Path Reconstruction
·      Travelling Salesman Problem (Using Bitmasking + DP)
·      Minimum Hamiltonian Cycle (Using Bitmasking + DP)
·      Finding Longest Simple Path in a Graph
·      Graph Isomorphism Check
·      Tree Decomposition of a Graph

 9. Grid and Matrix-Based Graph Problems
·      Number of Islands Problem (DFS/BFS)
·      Counting Connected Components in a Grid
·      Rat in a Maze Problem
·      Minimum Steps to Reach the End of a Grid
·      Knight’s Shortest Path in a Chessboard
·      Finding the Shortest Bridge Between Two Islands
·      Minimum Distance to Traverse All Points in a Grid
·      Path with Maximum Gold in a Grid
·      Count the Number of Enclaves in a Grid
·      Path with Maximum Sum in a Grid
 
 10. Miscellaneous Graph Problems
·      Course Schedule Problem (Topological Sort)
·      Alien Dictionary (Topological Sort in a Directed Graph)
·      Reconstruct Itinerary from Given Tickets (Eulerian Path)
·      Word Ladder Problem (BFS)
·      Minimum Swaps to Sort an Array Using Graph
·      Reconstructing a Binary Tree from Preorder and Inorder Traversals (Using Graph Concepts)
·      Steiner Tree Problem
·      Finding Safe States in a Graph
·      Graph-Based Recommendation Systems
·      Finding the Center of a Star Graph