I am posting an Open Graph story using the graph API but the post is not shown anywhere on my Facebook wall and there is nothing in my Activity Log either.
I configu
First at all you need to get approval for every item of your open graph story. You can test your application without approval un-publishing it and adding some user as testers in the Role settings.
Now, to see your open graph activity in your timeline after publish you should configure the Additional Capabilities for you action type. So you need to check the Explicitly Shared option in the Capabilities section for you action. After that you need to include the parameter fb:explicitly_shared=true in the open graph call.
You can take a look to the Additional Capabilities here : https://developers.facebook.com/docs/sharing/opengraph/using-actions#capabilities
Explicit shared should be added in the post parameters.