For the 1st question, you have 25 points labelled
Now you have to draw edges connecting the points. The rule you give is
and are connected iff gcd(n,m) > 1.
Recall that gcd(n,m) = greatest common divisor of n and m. (Think - what's the biggest integer that goes into both n and m?)
So let's try drawing edges. Do we draw an edge between
and ? No, because gcd(2,3) = 1.
and ? Yes, because gcd(2,4) = 2.
and ? Yes, because gcd(12,15) = 3.
and you should be able to keep on going.