Understanding Traversals in Graph Theory: Types and Applications

Traversed means that the algorithm visits every vertex in the graph, either once or multiple times, depending on the type of traversal. The goal of traversing a graph is to explore all the vertices and their connections, and to gain insights into the structure and properties of the graph.

There are several types of traversals, including:

1. Breadth-first traversal (BFS): starts at a given vertex and explores all vertices at the same distance before moving on to the next level.
2. Depth-first traversal (DFS): starts at a given vertex and explores as far as possible along each branch before backtracking.
3. Depth-limited search: combines elements of BFS and DFS, exploring a fixed depth before backtracking.
4. Cycle detection: checks for the presence of cycles in the graph.
5. Shortest path: finds the shortest path between two vertices in the graph.

Each type of traversal has its own applications and use cases, and they can be used to solve different types of problems in graph theory.