Algorithms | Graph Traversals | Question 12

Consider the following graph,

Among the following sequences:

(I) a b e g h f 
(II) a b f e h g
(III) a b f h g e 
(IV) a f g h b e  

Which are depth first traversals of the above graph?
(A) I, II and IV only
(B) I and IV only
(C) II, III and IV only
(D) I, III and IV only

Answer: (D)
Explanation: We can check all DFSs for following properties.

In DFS, if a vertex 'v' is visited
after 'u', then one of the following is true.
1) (u, v) is an edge.
     u
   /   \
  v     w
 /     / \
x     y   z

2) 'u' is a leaf node.
     w
   /   \
  x     v
 /     / \
u     y   z

In DFS, after visiting a node, we first recur for all unvisited children. If there are no unvisited children (u is leaf), then control goes back to parent and parent then visits next unvisited children.
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