Answer:
There are many algorithms that can be applied to graphs, depending on the problem and the goal. Some algorithms require you to perform the algorithm for each vertex in the graph, while others do not. Here are some examples of both types:
• Breadth-first search (BFS) is an algorithm that explores a graph by visiting all the vertices that are reachable from a given source vertex, in increasing order of their distance from the source. BFS requires you to perform the algorithm for each vertex in the graph, because it only finds the shortest paths from one source to all other vertices, not between any pair of vertices.
• Depth-first search (DFS) is an algorithm that explores a graph by visiting all the vertices that are connected to a given source vertex, following a path as deep as possible before backtracking. DFS requires you to perform the algorithm for each vertex in the graph, because it only finds one path from one source to any other vertex, not necessarily the shortest or all possible paths.
• Dijkstra's algorithm is an algorithm that finds the shortest paths from a single source vertex to all other vertices in a weighted graph, where the weights represent the distances or costs of the edges. Dijkstra's algorithm does not require you to perform the algorithm for each vertex in the graph, because it finds the shortest paths from one source to all other vertices in one run. However, if you want to find the shortest paths between any pair of vertices, you need to run Dijkstra's algorithm for each vertex as the source.
• Floyd-Warshall algorithm is an algorithm that finds the shortest paths between all pairs of vertices in a weighted graph, where the weights can be positive or negative, as long as there are no negative cycles. Floyd-Warshall algorithm does not require you to perform the algorithm for each vertex in the graph, because it finds the shortest paths between all pairs of vertices in one run.
These are just some examples of graph algorithms and whether they require you to perform them for each vertex in the graph or not. There are many more graph algorithms that can be used for different purposes and have different properties.
Explanation: