GO Classes Test Series 2024 | Discrete Mathematics | Test 5 | Question: 6

Answer 1

Since graph is finite directed acyclic graph so there must be some vertex with no incoming edge and there must be some vertex with no outgoing edge. C is not necessarily true.

Comments

@BHOJARAM

A and B are always true for any connected DAG. Also, DAG can have an isolated vertex with no edges and can be still connected

Given in the question that no. of edges is greater than 0 and so we have minimum 1 edge. So, there must be atleast two vertices in the graph connected by this edge

Now, if we have a third vertex which is isolated , it will disconnect the graph. So, no. of edges plays a vital role in deciding option C

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thanx for correction@sk91…

Yes,as given that |E|>0, so statements A and B are necessarily true...

 

 

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its not necessary to have an isolated vertex.