algorithm - Spanning Tree VS. Spanning Forest -


what's difference between spanning tree , spanning forest in graphs, conceptually.

also, possible construct spanning forest through dfs or bfs traversals? why? how?

i understand spanning tree, couldn't find clear explanations spanning forests. wikipedia (https://en.wikipedia.org/wiki/spanning_tree), doesn't give clear definition it. book (data structures & algorithms, wiley - sixth edition) has no definition spanning forests.

i wondering, if have graph example 3 connected components in it, possible construct spanning forest dfs/bfs traversals?

when there one connected component in graph, spanning tree = spanning forest.

but when there multiple connected components in graph. example in following picture have 3 connected components.:

enter image description here

so each component, have spanning tree, , 3 spanning trees constitute spanning forest

i wondering, if have graph example 3 connected components in it, possible construct spanning forest dfs/bfs traversals?

yes possible. when there 1 connected component, bfs or dfs terminate visiting vertices , have spanning tree (which in case equal spanning forest).

but when have more 1 connected component, in picture, thing have start bfs or dfs unvisited vertex. algorithm terminates when there no unvisited vertex left , each bfs or dfs traversal yield spanning tree.


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