NP$-$Completeness $($Sections $11\mathrm{.}3,12\mathrm{.}1,12\mathrm{.}2)[10$ points$]$

Give examples of the following graphs or explain why such examples cannot ex$-$

ist.

a$.$ graph with both a Hamiltonian circuit and an Eulerian circuit.

b$.$ graph with neither an Eulerian circuit nor a Hamiltonian circuit.

c$.$ graph with an Eulerian circuit but no Hamiltonian circuit. If you can find an

example, describe a polynomial$-$time algorithm on how to locate such an Eulerian

circuit. Show details of your answer.