1. Write a program to implement Dijkstra's algorithm for finding the shortest path in a weighted graph.
2. Create a function to perform a depth-first search (DFS) in a graph and return the traversal order.
3. Write a program to perform a breadth-first search (BFS) in a graph and return the traversal order.
4. Implement a function to detect cycles in a directed graph using DFS.
5. Write a program to find all strongly connected components in a directed graph using Kosaraju's algorithm.
6. Create a function to check if a graph is bipartite using BFS.
7. Write a program to find the shortest path in an unweighted graph using BFS.
8. Implement a function to find the minimum spanning tree (MST) using Prim's algorithm.
9. Write a program to find the articulation points in a graph.
10. Create a function to find the longest path in a directed acyclic graph (DAG).
11. Write a program to count the number of connected components in an undirected graph.
12. Implement a function to perform a topological sort of a directed graph.
13. Write a program to find the diameter of a tree.
14. Create a function to determine if a graph contains a Hamiltonian cycle.
15. Write a program to find the k-th shortest path in a weighted graph.
16. Implement a function to find the minimum cut in a flow network using the Ford-Fulkerson method.
17. Write a program to detect a cycle in an undirected graph using Union-Find.
18. Create a function to find the maximum flow in a flow network using the Edmonds-Karp algorithm.
19. Write a program to determine if a graph is a tree.
20. Implement a function to find the shortest path using the Bellman-Ford algorithm.
21. Write a program to find all bridges in a graph.
22. Create a function to find the minimum spanning tree using Kruskal's algorithm.
23. Write a program to check if two graphs are isomorphic.
24. Implement a function to calculate the transitive closure of a directed graph using the Floyd-Warshall algorithm.
25. Write a program to find the least common ancestor of two nodes in a binary tree.
26. Create a function to check if a graph is a complete graph.
27. Write a program to find the maximum bipartite matching using the Hopcroft-Karp algorithm.
28. Implement a function to find the Eulerian path in a graph.
29. Write a program to determine the in-degree and out-degree of each vertex in a directed graph.
30. Create a function to find the center of a tree.
31. Write a program to determine if a directed graph has a cycle using topological sorting.
32. Implement a function to find the shortest path between all pairs of vertices using the Floyd-Warshall algorithm.
33. Write a program to find the path with the maximum sum in a binary tree.
34. Create a function to check if a graph is strongly connected.
35. Write a program to find the maximum weight independent set in a graph.
36. Implement a function to generate the adjacency matrix from an edge list.
37. Write a program to find the longest common subsequence in two sequences using a graph approach.
38. Create a function to count the number of triangles in a graph.
39. Write a program to find the distance between two nodes in a tree using binary lifting.
40. Implement a function to determine if a graph can be colored using k colors.