Graph-theory-question - Advanced Questions

Topic: Graph-theory-question / Level: Advanced

550. Create a function to check if a bipartite graph has a perfect matching.
551. Write a program to compute the distance between all pairs of vertices using the Floyd-Warshall algorithm.
552. Implement an algorithm to find the longest path in a directed acyclic graph (DAG).
553. Write a program to check if a directed graph has a Hamiltonian path.
554. Create a function to compute the minimum spanning tree of a graph using Prim's algorithm.
555. Write a program to find the longest cycle in a directed graph.
556. Implement a function to determine the minimum number of edges needed to make a directed graph strongly connected.
557. Write a program to compute the betweenness centrality for a graph.
558. Create a function to find the shortest path in a directed graph with positive weights.
559. Write a program to check if a directed graph can be acyclic.
560. Implement an algorithm to find the minimum cost flow in a flow network.
561. Write a program to compute the reachability matrix of a directed graph.
562. Create a function to check if a bipartite graph has a unique perfect matching.
563. Write a program to find the longest alternating path in a graph.
564. Implement a function to compute the shortest path in a directed graph using Dijkstra's algorithm.
565. Write a program to check if a directed graph has a unique Hamiltonian cycle.
566. Create a function to determine the maximum independent set in a graph.
567. Write a program to compute the minimum spanning tree of a graph using Kruskal's algorithm.
568. Implement an algorithm to find the longest simple path in a directed graph.
569. Write a program to check if a directed graph can be partitioned into two subsets.
570. Create a function to compute the average distance between all pairs of vertices in a directed graph.
571. Write a program to find the shortest path in an undirected graph using the A* search algorithm.
572. Implement a function to determine the minimum cut in a flow network.
573. Write a program to compute the longest cycle in a bipartite graph.
574. Create a function to check if a directed graph has a unique longest path.
575. Write a program to find the longest increasing path in a grid.
576. Implement an algorithm to compute the maximum weight independent set in a bipartite graph.
577. Write a program to determine the number of connected components in a directed graph.
578. Create a function to find the longest simple cycle in a directed graph.
579. Write a program to check if a directed graph can be made strongly connected by adding edges.

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Create a function to determine the minimum cut in a flow network using the Stoer-Wagner algorithm. Write a program to calculate the degree distribution of a graph. Write a program to perform a breadth-first search (BFS) in a graph and return the traversal order. Write a program to check if a tree is a valid binary search tree. Write a program to check if a directed graph has a unique shortest path between two vertices. Write a program to find the maximum flow in a flow network using the Edmonds-Karp algorithm. Write a program to implement Dijkstra's algorithm for finding the shortest path in a weighted graph. Write a program to compute the reachability matrix of a directed graph. Write a program to compute the betweenness centrality for all vertices in a graph. Write a program to find the k-th shortest path in a weighted graph. Write a program to determine if a graph is a valid tree. Write a program to check if a graph can be colored with three colors. Implement an algorithm to compute the convex hull of a set of points. Write a program to find the longest cycle in a directed graph. Write a program to compute the betweenness centrality for a graph.