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The Breadth First Search algorithm has been implemented using the queue data structure. One possible order of visiting the nodes of the following graph is:

1. $MNOPQR$
2. $NQMPOR$
3. $QMNPRO$
4. $QMNPOR$
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1. MNOPQR: If you try to run BFS, after M, you must traverse NQR (In some order). Here, P is traversed before Q, which is wrong.
2. NQMPOR: This is also not BFS. P is traversed before O.
3. QMNPRO: Correct.
4. QMNPOR: Incorrect. Because R needs to be traversed before O.(Because M is ahead of N in queue).

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Option (c)   ------- QMNPRO    is correct.....what does it convey .....If it conveys " the shortest path from Q to every vertex in graph ", then how can we explain it ???
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Why option D not correct?

when we start BFS on Q vertex we get three nodes {M, N , P}  TO INSERT in QUEUE but these nodes can be any order because representation is not defined that why option D might be correct.
Ans- C

Option (A) is MNOPQR. It cannot be a BFS as the traversal starts with M, but O is visited before N and Q. In BFS all adjacent must be visited before adjacent of adjacent. Option (B) is NQMPOR. It also cannot be BFS, because here, P is visited before O. (C) and (D) match up to QMNP. We see that M was added to the queue before N and P (because M comes before NP in QMNP). Because R is M's neighbor, it gets added to the queue before the neighbor of N and P (which is O). Thus, R is visited before O.
In BFS using Queue data structure the correct option is C.

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