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[Solved]: Why BFS is source vertex specific?

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Problem Detail:

Take a graph \$G=(V,E)\$ .

As we know both DFS and BFS are graph search algorithms .

But why the algorithm for BFS is designed in such a way that it does not cares about the vertices that are not connected to the source vertex \$s\$ but DFS takes care about all vertices in \$V\$.

I mean if \$G\$ has \$l\$ connected components and a vertex \$s\$ is in one of the connected component among \$l\$ , then if \$s\$ is the source vertex for BFS , then BFS performs only traversal on the only one connected component (which contains \$s\$).

If \$G\$ is input for BFS , it constructs one BFS tree (for component which contains \$s\$).

But in case of DFS , it constructs a DFS forest with \$l\$ DFS trees.

Why no BFS forest and it is restricted to a specifc component (containing \$s\$)? Any reason involved ?

For Bfs algorithm page # 595 and for Dfs algorithm page # 604 from here

Both BFS and DFS are algorithms for exploring a single connected component, and there are also several others. All such algorithms can be extended to explore all connected components in a graph.