the relation between number of back edges and number of cycles in dfs is
Answers
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.
Explanation:
Back edge: It is a side (u, v) such that v is the ancestor of side u however now no longer a part of the DFS tree.
Edge from 6 to two is a returned side.
The presence of returned side shows a cycle in directed graph.
Cross Edge: It is a side that connects nodes such that they do now no longer have an ancestor and a descendant dating among them.
The edges we traverse as we execute a depth-first seek may be categorised into 4 side types.
During a DFS execution, the category of side (u, v), the threshold from vertex u to vertex v, relies upon whether or not we've got visited v earlier than withinside the DFS and if so, the connection among u and v.