Looking for some tutorials / references that discuss Breadth First Search that takes into consideration the cost of paths, but could not find much information.
Could someone refer a tutorial?
From a general point of view: there are tons, but I do sincerely recommend you the latest volume on Heuristic Search: Heuristic Search: Theory and Applications by Stefan Edelkamp and Stefan Schroedl.
From a specific point of view: in spite of the graph being directed or not, breadth-first search taking costs into account
Hope this helps,