... to write the initials of a person is as follows:
M.K. Gandhi - Correct
M K Gandhi - Correct (or rather, considered acceptable these days; but remember, the space is necessary)
M.K Gandhi - Incorrect!
Remember, initials are after all abbreviations, and M.K doesn't really suggest anything. Nor does Vijitha.V!
Speaking of which, when you write JFK, it is fine to write it without the periods!
(Confused? English is confusing!)