Is finding if a graph has k isolated nodes a NP-Complete problem?
No, determining whether a graph has $k$ isolated vertices is not1 NP-complete. Just count the number of isolated vertices and compare against&nbsp;$k$. This can be done deterministically in linear time (linear in the size of the graph's description; possibly quadratic in the number of vertices).

1 Unless P=NP and, even then, it might not be NP-complete.