How to evolve a graph with only one loop

1. how to continue to add new nodes to a graph with only one loop
would like to use graph traversal like my previous post to traversal a binary tree, but this time, it can 
loop forever, i mean it traverse all nodes in whole graph in the meanwhile it add new nodes too
assume maximum number of joint is 2 or 3
computing nightmare

I just realised that you weren't talking about cyclic graphs (in the case of 1 cycle) here, but meant a single pass traverse and mutate.
What you don't specify is how the new nodes are being supplied.  If they are supplied up front, then the loop will of course terminate once all the inputs are addressed, rather than going on forever.  If they are being supplied from time-to-time,
then you need to have some sort of event-wait on input.  The traversal could have a move-next something like this
If at end of tree with no new nodes, wait for input
If at end of tree, with input, reset to start
If at insertion point for new node at top of input queue, insert that
Move to next node in tree
This seems the sort of thing that would naturally be coded in a functional language as a tail recursion rather than an iteration.

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    I made an appointment with a Mac Genius and I will say that while it was better than getting to talk to India on a poor quality phone call it was just about as helpful. Sure she was cute and friendly, but I left without my issue resolved and was surprised that I didn't even get a followup from anyone asking about my experience (hence my venting here)
    Anyway, I found a solution for my issue here: http://tinyfish.net/2008/07/18/how-to-sync-iphone-with-multiple-computers/
    This is a real solution to the issue, and has the benefit that I can do this to as many machines as I need and sync at any of them instead of just one. Hopefully, Apple doesn't delete my response since it truly is the answer to the problem and others might be looking for the same solution.

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