Cut vertices and cut edges - did I answer these correctly? Problem
Find the cut vertices and cut edges for the following graphs

My understanding of the definitions:
A cut vertex is a vertex that when removed (with its boundary edges) from a graph creates more components than previously in the graph.
A cut edge is an edge that when removed (the vertices stay in place) from a graph creates more components than previously in the graph.
My Answers
31) The cut vertex is $c$.  There are no cut edges.
32) The cut vertices are $c$ and $d$.  The cut edge is $(c,d)$ 
33) The cut vertices are $b, c, d$ and $i$.  The cut edges are: $(a,b)$,$(b,c)$,$(c,d)$,$(c,e)$,$(e,i)$,$(i,h)$
For anyone reading this at a later date:
33) is wrong, per the answers and comments below, e is a cut vertex, not d

You're correct except that in $33$, $d$ is not a cutvertex and $e$ is.
