To switch beyween two Facebook accounts, you have to posses more than one Facebook account that logged in on The Graph application.
If you haven’t completed that step, follow these steps: How to Add Facebook Account on The Graph Mobile
Here are the steps to switch your Facebook accounts on The Graph Mobile:
1. Open Timeline Menu/ Facebook
2. Click sub-menu account/ people’s picture on top right
3. Select an account that you want to change; green sign next to the account shows that the account is active.