Graph-theory-question - Advanced Questions

Topic: Graph-theory-question / Level: Advanced

460. Implement an algorithm to find the minimum cost to connect all points in a graph.
461. Write a program to determine the maximum independent set in a graph using branch and bound.
462. Create a function to find the number of spanning trees in a graph using Kirchhoff's theorem.
463. Write a program to check if a directed graph is strongly connected.
464. Implement a function to compute the degree of separation between two nodes.
465. Write a program to find the longest alternating path in a binary tree.
466. Create a function to find the number of walks of length k in a directed graph.
467. Write a program to find the maximum flow using the Push-Relabel algorithm.
468. Implement an algorithm to find the all-pairs maximum flow in a flow network.
469. Write a program to compute the minimum path cover in a directed acyclic graph.
470. Create a function to calculate the reachability matrix of a graph.
471. Write a program to determine the minimum number of colors required to color a graph.
472. Implement a function to find the smallest spanning tree in a graph with negative weights.
473. Write a program to find the center and radius of a tree.
474. Create a function to compute the directed acyclic graph induced by a directed graph.
475. Write a program to find the longest path in an undirected graph using depth-first search.
476. Implement an algorithm to solve the Max-Cut Problem using randomized methods.
477. Write a program to compute the stability of a graph.
478. Create a function to check if a bipartite graph has a perfect matching.
479. Write a program to find the minimum spanning tree of a graph with random weights.
480. Implement a function to compute the kernel of a graph.
481. Write a program to find the minimum distance required to travel from one vertex to another in a graph.
482. Create a function to compute the girth of a graph.
483. Write a program to find the shortest path in a weighted graph using the Bidirectional Dijkstra's algorithm.
484. Implement an algorithm to detect and report strongly connected components in a directed graph.
485. Write a program to calculate the network flow between multiple sources and sinks.
486. Create a function to find the degree of each vertex in a weighted graph.
487. Write a program to find the minimum path sum in a triangle represented as a graph.
488. Implement a function to compute the minimum number of edge-disjoint paths in a graph.
489. Write a program to find the longest path in a weighted graph with negative weights.

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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.