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DM - Grand Test -Q8


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+1 vote
Which of the following is NOT a sufficient and necessary condition for an undirected graph G to be a tree ?(n is the number of vertices in G)

(A) G is connected and has n-1 edges.

(B) G is acyclic and connected.

(C) G is acyclic, connected and has n-1edges.

(D) G has n-1 edges.
asked Aug 30, 2020 by gbeditor-2 (72,840 points)
reshown Aug 31, 2020 by gbeditor-2

2 Answers

+1 vote
 
Best answer
A) G is connected and n-1 edges this is neccessary and sufficient condition  as to connect any graph min edges will be n -1 and hence no cycle is possible so its is tree

B) G is acyclic and connected   this is the basic definition of tree with no cycle and connected a graph is always a tree

C) G is acyclic, connected and has n-1edges . it is a restatement of A  

D) G has n-1 edges  is a necessary but not  sufficient condition as a cycle is possible and then  graph will be disconnected

D is the right ans
answered Sep 9, 2020 by (18,750 points)
selected Sep 30, 2020 by deepak-gatebook
+1 vote
Option D can be a graph where one component is cycle and one is a path. then only n-1 edges is possible. But we cannot say that this graph is a tree because a cycle exists.

Therefore it is necessary but not sufficient.
answered Sep 30, 2020 by tsshashankrustagi (11,240 points)
Answer:

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