We are starting from $s.$
- $(s-w)$ and $(s-z)$ are possible edges to traverse to. Since the vertex earlier in the alphabetical order is to be chosen $(s-w)$ will be chosen as the first tree edge. $z$ stays in the stack behind $w.$
Now, $w$ is the next vertex from the stack.
- $(w-x)$ becomes a next tree edge.
$x$ is the next vertex from the stack.
- $(x-z)$ becomes a next tree edge.
$z$ is the next vertex from the stack.
- $(z-w)$ becomes a back edge as $w$ is already visited.
- $(z-y)$ becomes a next tree edge.
- $(s-z)$ becomes a forward edge.
$y$ is the next vertex from the stack.
- $(y-x)$ becomes a back edge as $x$ is already visited.
All the vertices in stack are now visited. Any of the remaining $3$ vertices are the possible choices now and as we are following alphabetical order $t$ will be chosen next.
- $(t-u)$ becomes a tree edge and $v$ stays behind $u$ in the stack.
$u$ is the next vertex from the stack.
- $(u-t)$ becomes a back edge as $t$ is already visited.
- $(u-v)$ becomes a tree edge.
$v$ is the next vertex from the stack.
- $(v-s)$ and $(v-w)$ become cross edges as both $s$ and $w$ are visited earlier but both are not having a path to $v.$
- $(t-v)$ becomes a forward edge.
All vertices are covered.
- Tree edges: $\{(s-w), (w-x), (x-z), (z-y), (t-u), (u-v) \}$
- Back edges: $\{(z-w), (y-x), (u-t)\}$
- Forward edges: $\{(s-z), (t-v) \}$
- Cross edges: $\{(v-s), (v-w)$
So, correct answer is A.
https://cs.stackexchange.com/questions/11116/difference-between-cross-edges-and-forward-edges-in-a-dft
https://courses.csail.mit.edu/6.006/fall11/rec/rec14.pdf
