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.