Find the fundamental groups of graphs A, B and C as shown:
They look simple but I am unsure what their fundamental groups would be.
I was thinking that $A$ and $B$ are generated by just one element so $\pi(A)=\pi(B)=\mathbb{Z}$. Is this correct?
It would be good to get some insight into the ideas ebhind this problem so I can understand what is going on
$\pi_1(A)$ and $\pi_1(B)$ are trivial since they are contractible, $\pi_1(C)$ is the free group generated by 2 elements since $C$ retract to the bouquet of two loops.