GATE | GATE-CS-2003 | Question 21

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: DFS of a graph

1) Visits a node. 
2) Do following for every unvisited adjacent.
   a) Completely explores all vertices through current 
      adjacent using recursive call to DFS.

There can be any DFS possible as we may pick different vertices as starting points and we may pick adjacents in different orders.

(i) a b e g h f [Visit a, explore all adjacents through b, and so on..]. In this b’s adjacent e is picked first
(iii) a b f h g e [Visit a, explore all adjacents through b, and so on..]. In this b’s adjacent f is picked first
(iv) a f g h b e [Visit a, explore all adjacents through f, and so on..]. In this f’s adjacent g is picked first

(ii) a b f e h g can not be an answer as e is visited after f [e is not an adjacent of f and all adjcents of f are not explored yet]

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