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GATE | GATE 2017 Mock | Question 63

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Let G be a simple graph with 20 vertices and 8 components. If we delete a vertex in G, then number of components in G should lie between ____. (A) 8 and 20 (B) 8 and 19 (C) 7 and 19 (D) 7 and 20

Answer: (C)

Explanation: Case 1: If the vertex we are deleting from G is an isolated vertex, which is a component by itself, then number of components in G becomes 7.
Case 2: If G is a start Graph, then by deleting the cut vertex of G, we get 19 components.
Hence, number of components in G should lie between 7 and 19.

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Last Updated : 28 Jun, 2021
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