Option A is true.
Let us take a K4. It is both complete and planar.
Its linear graph will be a square pyramid which is neither complete nor planar.
So, both Q and R is false.
Let us take a 7 vertex binary tree.
The linear graph of this tree will be
So, S is also false.
Now for S, let us take a C6.
The linear graph of C6 will be
So, only P is true.