GATE | GATE-CS-2006 | Question 48

Let T be a depth first search tree in an undirected graph G. Vertices u and n are leaves of this tree T. The degrees of both u and n in G are at least 2. which one of the following statements is true?
(A) There must exist a vertex w adjacent to both u and n in G
(B) There must exist a vertex w whose removal disconnects u and n in G
(C) There must exist a cycle in G containing u and n
(D) There must exist a cycle in G containing u and all its neighbours in G.


Answer: (D)

Explanation: Below example shows that A and B are FALSE:
GATE_DFS2

Below example shows C is false:
GATE_DFS

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