[photon_lines]

You would only rotate a node when it becomes un-balanced (i.e. so the only case you would deal with is the instance where a new child-node is added to another child within the tree). There are no cases where you would need to re-balance when you add a 2nd child - the balance factor would be larger than 1 in the instance of adding the 1st child element to the node and thus you could never find cases like this (unless I'm misunderstanding what you're asking).

[rrobukef]

In the case of 3 with children 1 and 5 and 5 with children 4 and 6. 3 and 5 have two nodes. If you add 7 as a child of 6, the tree is unbalanced. This is not one of the cases shown.