I bought an iphone 5 unlocked from verizon. Can i use it in Greece with vodafone carrier?

It would be best to purchase an officially unlocked iPhone 5 in any EU country, rather than purchase one in the US. You purchase any US iPhone, & you will have no warranty/support in Greece & LTE will not be available. Doesn't make any sense, to me, to purchase a US iPhone, unless you live in the US & intend to use it in the US or the iPhone simply isn't sold where you live. In your case, buy your phone in the EU.

The iPhone 5 is not yet available in greece.

In which case neither will the nano sims used by the iPhone 5

It's your money, do what you like. If you insist on purchasing a US iPhone 5, you want the officially unlocked model. That model is currently unavailable in the US, & no one here would know when it will be available. When it is available, it will only be sold in Apple stores or the online Apple store...NO WHERE ELSE.

Good luck.

Verizon is cdma - no sims card Att is simms card based I would contact Vodaphone and get their opinion of the situation (i believe there technology is sims based) http://www.vodafone.co.uk/personal/index.htm to help you make the correct decision.

I would also explore the unlocked option with them (greece vodaphone) and a states based carrier (att) so you can use the phone in the states and eu if you travel

You need the A1429 model which is the one being sold in Greece. Even with A1428 you will not have 4G/LTE.