GATE | GATE 2017 Mock | Question 63

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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