spanning trees – Drawing a graph if all conditions are met

Let $G(V,E), V={1,2,3,4,5}$.
Draw a graph that satisfies all of the following conditions:

  1. G is an undirected connected graph.
  2. For every node v∈V, in the spanning tree received by BFS(v), deg(v)=2.
  3. For every node v∈V, in the spanning tree received by DFS(v), deg(v)=2.

I was trying to draw many graphs but none of them satisfied all of the conditions.
I was also trying to disprove that such a graph exists, but couldn’t find any strong claim that I could use for my proof.

Can you give me a hint?