GATE | GATE-CS-2003 closed

Question

Let G be an arbitrary graph with n nodes and k components. If a vertex is removed from G, the number of components in the resultant graph must necessarily lie between
(A) k and n
(B) k – 1 and k + 1
(C) k – 1 and n – 1
(D) k + 1 and n – k

The answer is C  . how is it k-1?? 

I  mean if we have only one component .?Please explain

Comments

if you have only one component means k=1 then suppose you have a graph which has only one vertex(n=1) then after deleting it how many components will be remaining ?