Articulation vertex in complementary graph How can I prove that if v is an articulation vertex in a graph G , that it will not be an articulation vertex in G' complimentary graph ? I know that an articulation vertex , is one which when removed disconects the G . And that the complementary graph , is one with two distinct vertices adjacent if and only if they are not adjacent in G.But I can't figure out how to connect this statements with my problem.

Let $X$ be one component of $G-v$ and $Y$ the rest of $G-v$. There are no edges between $X$ and $Y$ in $G$, so in $G'$ every vertex in $X$ is connected to every vertex in $Y$.

This means that $G'-v$ contains a complete bipartite graph, i.e. it is certainly connected, so $v$ cannot be an articulation vertex in $G'$.