Asymptotic time complexity for graph

I recently started learning about the graph and certain algorithms. REACH(G,s,t,n,i), COUNT(G, s, ni−1, i), UCONN(G, s, t).

The assumption in the textbook is for guessing a vertex, taking a vertex, or comparing two vertex will time O(log) time.

  1. for Reach I believe it would be O(nilogn)
  2. for Count it would be O(n^2ilogn)
  3. for UCONN it would be O(n^3logn)

Am I correct?