I was reading Application of DFS from here where I came to a statement which I cannot really understand. Would anybody mind explaining this to me.
For an unweighted graph, DFS traversal of the graph produces the minimum spanning tree and all pair shortest path tree.
My doubt: Is there anything "Minimum spanning tree" for unweighted graph. I mean after all it is unweighted so what is sense of MST here? And I completely don't understand how DFS produces all pair shortest path. Would anybody mind elaborating this a bit.