# Data Structures: Question Set – 29

#### What is graph isomorphism?

Graph isomorphism is the problem of determining whether two graphs are structurally identical, i.e., whether they have the same number of vertices, the same edges, and the same connectivity. Graph isomorphism is a difficult problem, and there is no known efficient algorithm for solving it in general.

#### What is Depth-First Search (DFS)?

Depth-First Search (DFS) is an algorithm used to traverse a graph or tree. It starts at a given vertex and explores as far as possible along each branch before backtracking.

#### What is the time complexity of DFS?

The time complexity of DFS is O(V+E), where V is the number of vertices and E is the number of edges in the graph.

#### How is DFS different from Breadth-First Search (BFS)?

DFS explores the graph by going as deep as possible along each branch, whereas BFS explores the graph by visiting all vertices at a given depth before moving on to the next depth.

#### What is a depth-first search tree?

A depth-first search tree is a subgraph of the original graph that is generated by DFS. It is a tree in which each vertex is connected to its parent in the search tree by a single edge.

#### What is backtracking in DFS?

Backtracking in DFS is the process of undoing a decision made by the algorithm and exploring a different path. This is done when the current path does not lead to a solution.

#### What is the purpose of marking vertices as visited in DFS?

Marking vertices as visited in DFS is necessary to avoid cycles and ensure that all vertices are visited once and only once.

#### Can DFS be used to find shortest paths in a weighted graph?

DFS can be used to find shortest paths in an unweighted graph, but it is not suitable for finding shortest paths in a weighted graph.

#### What is the difference between pre-order, in-order, and post-order traversal in DFS?

In pre-order traversal, the root node is visited first, then the left subtree, and finally the right subtree. In in-order traversal, the left subtree is visited first, then the root node, and finally the right subtree. In post-order traversal, the left subtree is visited first, then the right subtree, and finally the root node.

#### Can DFS be used to detect cycles in a graph?

Yes, DFS can be used to detect cycles in a graph. If a back edge is encountered during DFS, it means there is a cycle in the graph.