Memory Addresses of tree graphs and "transversal codes"

[thefatron]

Hello, I am new to computer science and would just like to ask a  couple of questions about tree graphs.

I am thinking about how you find different nodes on the same tree and record the path between them. 

Firtsly is there a recognised way of creating unique addresses for the nodes eg for a binary tree the address of the first node being the bit 0, left nodes from there adding zero and right nodes adding 1. This would mean all nodes would have there own unique number on the tree. This would work for creating unique addresses but is there another tequnique that comes with extra functionality?

I am trying to think of a test where we have two nodes with their addresses from the same tree and we have to find a path between them to prove that they do exist on the same tree? And not only find the path between them but collect some sort of "transversal code" which when compared to the account addresses will give a correct answer (this isnt very well explained, sorry)? Similar to the edcsa, node_addresses + transversal code = correct. 

 

If you can be bothered to try and answer that mess it would be greatly appreciated.

 

Cheers.