# 6.2 Isolated Vertex Detection

Isolated vertices are detected during a depth-first traversal of a graph. The detection scheme is based on the observation that an isolated vertex processed by dfs increases the depth-first number by exactly one. Algorithm 10 implements this observation in the main loop of a depth-first traversal (Algorithm 8). It assumes the buffer $v$ provides communication with the vertex list.

Algorithm 10: Isolated Vertex Detection
 $dfn=0$ $k=$first($V$) while $k\neq eol$ if evaluate($\gamma,v$) is $unvisited$ $depth=0$ $i=dfn$ dfs($v$) if $dfn$ is $i+1$ isolated vertex $k=$next($V,k$)

Since the isolated vertex test is an O(1) operation, it does not increase the complexity of a depth-first traversal.