Applications of Depth First Search

Depth-first search (DFS) is an algorithm (or technique) for traversing a graph.

Following are the problems that use DFS as a building block.  

1) Detecting cycle in a graph 
A graph has cycle if and only if we see a back edge during DFS. So we can run DFS for the graph and check for back edges. (See this for details)

Applications of Depth First Search: https://www.geeksforgeeks.org/applications-of-depth-first-search/