I just wanted a bit of clarification on the above picture. I understand the general idea of building out a tree in DFS order and stopping once you come across a number bigger than you got before. For example, when the value of the path becomes $ 14$ or $ inf$ the algorithm stops because there was already a path of value $ 11$ . But, I am quite confused with regards to where these numbers are coming from (the lower bounds on the cost). For example, the path from vertex $ A$ to vertex $ B$ has length $ 1$ , but in the tree, the path from $ A$ to $ B$ has a lower bound of $ 10$ .

So, I would greatly appreciate if anyone could let me know where the numbers in the branch-and-bound search tree are coming from!