Testbook Test Series

Question

Comments

Answering in comment section for quicker response. The sequence in option 1 cannot be a sequence of a graph. Hence i think option 1

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why option A not a sequence of a graph ?

 

btw either for comment or answer, you get the response in same time.

Answer 1

The question is a little ambiguous since it is not mentioned whether the graph is a connected graph or otherwise, since the first sequence is not possible for a connected graph. But looking at the options I think the question implicitly assumes the graph may not be connected.

The answer should be option 3.

For the first sequence, this can happen if we have three connected components each with 2 vertices. Hence degree of each vertex would be 1.

For the second sequence, 222222. This can happen in a cyclic graph of 6 vertices.

For the fourth option. 321110. This can happen if we have a graph having two connected components, one having 5 vertices say v1, v2, v3, v4, v5. And the other having only one vertex hence trivially connected. Let v1 be connected to v2, v3 and v4. v2 be connected to v1 and v5. This component has the degree sequence of 3,2,1,1,1. Thus we have a graph having such a degree sequence.

For the third option it is impossible to divide the degree sequence of 3,3,3,1 into connected components. Hence this is the correct option