On the Wiki and UESP, it says you can use weapons and shields to effectively use the Block Skill, which is obvious. On the Wiki, it says two-handed weapons are affected by the right side of the Block tree when blocking with them.

I was wondering if it's the same for One-handed weapons as well. (The right side of the tree consists of Power, Deadly, and Disarming bashes.)

I don't think so, as I'm pretty sure a single 1H weapon will only equip to the right hand - you can't choose to switch it to your left - and IIRC blocking moves can only be performed with the left hand (or with both hands if a 2H weapon is equipped). If you have a shield or torch in the left any blocking will be done with that, not your weapon, and if you have two 1H weapons equipped you can't block at all.

yes they perform well with a shield.

Neither of you answered his question. He wants to know if the bash perks that apply to bashing with a two handed weapon (on the right side of the 'block' perk tree) also work while you use a shield and sword. My sense is that the answer is 'no', but if you were just using a one handed sword without a shield then they would apply. But I don't know this for a fact.

You could level up, save, get one of the perks, and then test it with a sword an shield. Then reload your save if you are dissatisfied with the results.

You can block just fine with a 1h weapon, just need to have the left hand empty.
As for the topic, I don't see why they wouldn't work the same way, so Shield Wall, Quick Reflexes, Power Bash, Deadly Bash, Disarming Bash and Block Runner should work, while Deflect Arrows, Elemental Protection and Shield Charge only work with shields.
I haven't tested it though.

All the block perks work with shields.

I think the question is whether the skills that are said to effect blocking with just a two-handed weapon would also effect blocking with just a one-handed weapon. As in, no shield or torch. You have an empty off-hand, and are blocking with your weapon. As far as I know, they do, but I'm not entirely sure.

Interesting, the UESP says that blocking can only be done with whatever is in the left hand, or both hands in the case of a 2H weapon. This would seem to rule out any form of blocking with a single 1H weapon, since it will by default be equipped to the right hand. Yes, if you have a shield or torch equipped in the left, you can block while wielding a 1H weapon - but the block will be done on the left, with the shield or the torch, not the weapon.

I'm curious if anyone can confirm playing with a 1H weapon on the right and an empty left hand and being able to block on the right with the weapon.