# Is there any maximal 1-planar or 2-planar graph that is not 3-connected

A graph is $$k$$-planar if it can be drawn in the plane so that each edge is crossed at most $$k$$ times. A $$k$$-planar graph $$G$$ is maximal if $$G+uv$$ is not $$k$$-planar for any non-adjacent vertices $$u,v\in V(G)$$.

• Is there any maximal $$1$$-planar graph that is not $$3$$-connected ?
• Is there any maximal $$2$$-planar graph that is not $$3$$-connected ?

I believe those examples exist but didn't find any references mentioned this.