Let T be a depth first search tree in an undirected graph G. Vertices u and ν are leaves of this tree T. The degrees of both u and ν in G are at least 2.
In such case in the graph there will be two cycles :- One Cycle will contain u and other one v.
There cannot be a graph containig a single cycle and containing both u and v and also satisfy above Constraint.
Am I right?