An undirected graph is called connected if there is a path from every node to every other node. An edge is called a connector if the graph after removal of the connector is no longer connected. Recall that in an undirected graph, there are only tree edges and back edges after DFS$.$

$($a$)$ Show that a back edge can never be a connector.

$($b$)$ Show that a tree edge $\backslash (($u$,$ v$)\backslash )$ is a connector if and only if there are no back edges that connect a descendant of $\backslash ($ v $\backslash )$ to an ancestor of $\backslash ($ u $\backslash ).$