# Tree, Back, Edge and Cross Edges in DFS of Graph

Consider a directed graph given in below, DFS of the below graph is 1 2 4 6 3 5 7 8. In below diagram if DFS is applied on this graph a tree is obtained which is connected using green edges.

**Tree Edge**: It is a edge which is present in tree obtained after applying DFS on the graph. All the Green edges are tree edges.

**Forward Edge**: It is an edge (u, v) such that v is descendant but not part of the DFS tree. Edge from **1 to 8** is a forward edge.

**Back edge**: It is an edge (u, v) such that v is ancestor of edge u but not part of DFS tree. Edge from **6 to 2** is a back edge. Presence of back edge indicates a cycle in directed graph.

**Cross Edge**: It is a edge which connects two node such that they do not have any ancestor and a descendant relationship between them. Edge from node **5 to 4** is cross edge.

## Recommended Posts:

- Maximum Possible Edge Disjoint Spanning Tree From a Complete Graph
- Maximum number of edges to be added to a tree so that it stays a Bipartite graph
- Ways to Remove Edges from a Complete Graph to make Odd Edges
- Remove all outgoing edges except edge with minimum weight
- Edge Coloring of a Graph
- Program to Calculate the Edge Cover of a Graph
- Check if removing a given edge disconnects a graph
- Maximize number of nodes which are not part of any edge in a Graph
- Shortest Path in a weighted Graph where weight of an edge is 1 or 2
- Count number of edges in an undirected graph
- Number of Simple Graph with N Vertices and M Edges
- Minimum number of edges between two vertices of a graph using DFS
- All vertex pairs connected with exactly k edges in a graph
- Maximum number of edges in Bipartite graph
- Minimum number of edges between two vertices of a Graph

If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

Please Improve this article if you find anything incorrect by clicking on the "Improve Article" button below.