Edge which connects a vertex to an ancestor in the DFS tree is termed asa)Back edgesb)Cross edgesc)None of the mentionedd)Forward edges

Understanding the Types of Edges in Graphs

In graph theory, particularly in depth-first search (DFS), different types of edges are classified based on how they connect the vertices. Here’s a breakdown of the options provided:

1. Back Edges: An edge that connects a vertex to one of its ancestors in the DFS tree. This creates a cycle.

2. Cross Edges: These edges go between two vertices that are neither in a direct ancestor-descendant relationship, meaning they connect nodes across different branches of the DFS tree.

3. Forward Edges: An edge that connects a vertex to one of its descendants in the DFS tree.

4. None of the Mentioned: This option implies the possibility that none of the definitions correspond to the statement.

Conclusion

Based on the definitions above, the edge which connects a vertex to an ancestor in the DFS tree is termed Back Edges.

Final Answer

a) Back edges