 DFS discovery time

The DFS discovery time of a vertex is its first-visit number in depth-first search, assigned by an increasing counter. Discovery edges form a rooted tree in each connected component of a graph. For the joined-$CD$ example, starting at $A$ and visiting graph neighbours in lexicographic order gives first visits $A,B,C,D,E,F$, numbered $1,2,3,4,5,6$; its discovery edges are $AB,BC,CD,DE,EF$. These numbers encode the chosen traversal, not an invariant of the graph.