The Breadth First Search explores every node once and put that node in queue and then it takes out nodes from the queue and explores it's neighbors.

When Every node will have one successor then the Breadth First Search is unique. In all other cases, when it will have more than one successor, it can choose any of them in arbitrary order.

The Breadth First Search will make a graph which don't have back edges (a tree) which is known as Breadth First Tree.

Breadth First Search can be applied to all of the mentioned problems. Bipartiteness of a graph means that a graph can be divided into two disjoint sets such that every edge connects a vertex in to one in.

This is the definition of the Breadth First Search. Exploring a node, then it's neighbors and so on.

The Depth First Search is implemented using recursion. So, stack can be used as data structure to implement depth first search.

The Depth First Search will make a graph which don't have back edges (a tree) which is known as Depth First Tree.

Depth First Search can be applied to all of the mentioned problems.

This is the definition of the Depth First Search. Exploring a node, then aggressively finding nodes till it is not able to find any node.

When Every node will have one successor then the Depth First Search is unique. In all other cases, when it will have more than one successor, it can choose any of them in arbitrary order.