Complete Bipartite Graph, Euler and Hamiltonian Circuit

Question

I just need some confirmation on if these Complete Bipartite Graph are Euler Circuit and Hamiltonian Circuit.

$K_{1,1}$ --> Not Euler Circuit (Odd Degree) and Not Hamiltonian

$K_{1,2}$ --> Not Euler Circuit (Odd Degree) and Not Hamiltonian

$K_{2,2}$ --> Is Euler Circuit and is Hamiltonian

$K_{1,3}$ --> Not Euler Circuit (Odd Degree) and Not Hamiltonian

Thanks

Answer 1

Looks correct to me. Also, $K_{1,1}$ and $K_{1,2}$ have Euler/Hamiltonian paths; $K_{1,3}$ has nothin'.