What you are looking for is called "actions". Here is how to post an action.
// create an Open Graph action
id<FBOpenGraphAction> action = (id<FBOpenGraphAction>)[FBGraphObject graphObject];
[action setObject:objectId forKey:@"dish"];
// create action referencing user owned object
[FBRequestConnection startForPostWithGraphPath:@"/me/fbogsample:eat" graphObject:action completionHandler:^(FBRequestConnection *connection, id result, NSError *error) {
if(!error) {
NSLog([NSString stringWithFormat:@"OG story posted, story id: %@", [result objectForKey:@"id"]]);
[[[UIAlertView alloc] initWithTitle:@"OG story posted"
message:@"Check your Facebook profile or activity log to see the story."
delegate:self
cancelButtonTitle:@"OK!"
otherButtonTitles:nil] show];
} else {
// An error occurred
NSLog(@"Encountered an error posting to Open Graph: %@", error);
}
}];
However, before you post a question about Facebook open-graph in general, you should check here first.