[Algorithms] BFS Back edges

Question

True / False?

1. For a directed graph, the absence of back edges with respect to a BFS tree implies that the graph is acyclic.

2. The depth of any DFS tree rooted at a vertex is at least as much as the depth of any BFS tree rooted at the same vertex.

Comments

https://courses.csail.mit.edu/6.006/oldquizzes/solutions/q2-s2010-sol.pdf

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I got the question from the link you shared above:).I didn`t get the explanation there ,thats why i posted here

Can you share an example tree for which there are no back edges in BFS but still cycle is there?

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@ papesh can you please give example of statement 1

Answer 1

Both Statement are correct.

The below Image shows a Graph G and BFS is applied on G. and a back edge that shows a cycle.

Comments

what is back edge. plz explain more.

And also explain for:If there is DFS in place of BFS.

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But the answer is given only 2 is correct.