Discovery Time

Discovery time disc[v] is the timestamp when DFS first visits vertex $v$. The first vertex visited gets disc[v] = 0, the next gets $1$, and so on. Discovery times create a total order on vertices based on when DFS reaches them.

If $u$ is an ancestor of $v$ in the DFS tree, then disc[u] < disc[v]. But the reverse is not always true. A node discovered earlier might be in a different subtree, not an ancestor. To confirm ancestry, you also need the finish time: $u$ is an ancestor of $v$ if and only if disc[u] < disc[v] < fin[u].