Question

What does the bfs tree tell us about the distance form one vertex to another when neither is at the root?

Answer 1

Each vertex in a breadth-first search is given one of two values:

• A distance indicates the least amount of edges needed to travel from source vertex to vertex vvv.
• Following some shortest path from the source vertex, the predecessor vertex of vvv.
• The predecessor of the source vertex is some unique value, such as null, indicating that it has no predecessor.

The distance between vvv and the source vertex is infinite if there is no path connecting them, and their predecessors have the same special value.

Here is an undirected graph with eight vertices, each of which is numbered from 0 to 7, with the vertex numbers either above or below the vertices. Each vertex contains two numbers: vertex 3, which is the distance from the source, and vertices

The following are some uses for BFS:

- Cheney's algorithm for garbage collection imitation.

- Determining the shortest path between nodes u and v, with the length of the path being determined by the number of edges (an advantage over depth-first search).

- Verifying the bipartiteness of a graph.

- Unweighted graph's minimum spanning tree.

 website crawler.

- Locating nodes in any connected graph component.

- Ford-Fulkerson method for calculating a flow network's maximum flow.

- Binary tree serialization and deserialization.

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