Is Every Induced Subgraph with a Cut-Vertex a Block?

[voodoomathema]

If G is a connected graph with a cut-vertex v and G1 is a component of G-v, then show that the induced subgraph <V(G1)U{v}> of G need NOT be a block of G.

I guess all I would need is a counterexample, but I can't come up with one.

 

[Office_Shredder]

Think of some standard examples of graphs that aren't blocks. Try connecting two of them through a single vertex