I am developing one android application.
As we all know Facebook SDK provides functionality to send request to other users using Request Dialog.
https://develope
There is no way to post notification like facebook using google API. You can create a app activity using Google+ API that will post on the user's profile without explicit user action.By default its private & hidden. User must have to take share actions to make that visible. App activities are only visible to user because its not posted directly on stream like facebook or twitter. Hence you can not achieve the same result like facebook or twitter.
For posting the application activity you can use Google+ Moments: insert. It needs to get the permission using scope from user. For android sdk use can use Manage app activities in Google
Scopes:
https://developers.google.com/+/api/latest/moments/insert
https://www.googleapis.com/auth/plus.login
Using Google App Domain can automatically create a post with visibility limited to the user or circle. For posting the application activity you have to use Activities: insert
Scopes:
https://www.googleapis.com/auth/plus.stream.write
https://www.googleapis.com/auth/plus.me
Conclusion: You have to take a decision to use one of the API based on your requirement. I would suggest play with both the API to check the difference & its limitation in user profile. First try with Google+ Domain API as it will post message on user stream.