Question $3)$ Here is a proposal for how to find the length of the shortest cycle in an undirected graph with unit edge lengths: When a back edge, say $($v$,$w$)$ is encountered during a depth$-$first search, it forms a cycle with the tree edges from w to v$.$ The length of the cycle is level$[$v$]-$ level$[$w$]+1,$ where the level of a vertex is its distance in the DFS tree from the root vertex. This suggests the following algorithm:Do a depth first search, keeping track of the level of each vertexEach time a back edge is encountered, compute the cycle length and see it if it is smaller than the shortest one previously seen Show that this strategy does not always work by providing a counterexample as well as a brief $($one or two sentence$)$ explanation.