Let $\backslash ($T$\backslash )$ be the spanning tree rooted at the start vertex produced by the depth$-$first search of a connected, undirected graph $\backslash ($G$\backslash ).$ Argue why every edge of $\backslash ($G$\backslash ),$ noting $\backslash ($T$\backslash ),$ goes from a vertex in $\backslash ($T$\backslash )$ to one of its ancestors, that is$,$ it is a back edge. $\backslash \backslash$

Hint: Suppose that such a nontree edge is a cross edge, and argue based upon the order the DFS visits the end vertices of this edge.$\backslash \backslash$