Does leveling skills in Skyrim increase strength or do I need to buy the perks?

I am level 51 in one-handed combat. However, I still cannot kill Trolls, Giants and some "Bandit" leaders easily.

Do I need to buy perks to increase my strength? Or leveling only will guarantee my success?

Solution 1:

There is no strength in Skyrim. Increasing your skill with a weapon type will make your attacks with weapons of that type stronger, while buying some perks will make your attacks stronger or give you some new abilities (bleeding wounds with axes, bypassing armor with maces, beheading, etc).

Solution 2:

When I did armor rating research, I found that raising an armor skill to 100 gave about a +35% modifier, while the armor perks gave a +200% modifier (aka multiplied by 3). Skill levels serve mainly as a way to get character levels and perk points, and secondarily to gate perk spending. Perks are the main way to improve your character's capabilities. If you don't spend your perks, you will be very weak.

Solution 3:

As your skill level increases, the effectiveness of that particular skill increases slightly. ex. You will hit harder with one handed weapons at level 100 than at level 10. The perks in the one-handed tree also provide bonuses, so if you choose to spend points in that tree, you will perform better with one-handed weapons.