ECS122A Handout May 17, 2009
Depth-first search
DFS(G)
for each vertex u∈V
do color[u] = white
endfor
time = 0
for each vertex u∈Vdo
if color[u] = white then
DFS-visit(u)
endif
end for
DFS-visit(u)
color[u] = gray
time = time + 1
d[u] = time
for each v∈Adj[u] do
if color[v] = white then
DFS-visit(v)
color[u] = black
time = time + 1
f[u] = time
Classification of edges
•Tree edge (T): encounter new (white) vertex
gray to white
•Back edge (B): from descendant to ancester
gray to gray
•Forward edge (F): from ancestor descendant
gray to black
•Cross edge (C): any other edges
gray to black
Note: In an undirected graph, there may be some ambiguity since edge (u, v) and (v, u) are the
same edge. Classify by the first type above that matches. Therefore, if Gis undirected, a DFS
produces only tree (T) and back (B) edges.
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