Draw a graph on $5$ vertices that satisfies all of the following conditions:
- $G$ is an undirected connected graph.
- For every node $v∈V$, in the spanning tree received by BFS($v$), $\deg v=2$.
- 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?