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
$\endgroup$2 Answers
$\begingroup$You're correct except that in $33$, $d$ is not a cutvertex and $e$ is.
$\endgroup$ 0 $\begingroup$Good job except on 33) $d$ is not a cut vertix and $e$ is . and the cut edges are $(b,c) ,(c,e) ,(e,i)$ 32) and 31) seems correct for me .
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