<P> A theorem by Nash - Williams says that every k ‐ regular graph on 2 k + 1 vertices has a Hamiltonian cycle . </P> <Ul> <Li> <P> 0 - regular graph </P> </Li> <Li> <P> 1 - regular graph </P> </Li> <Li> <P> 2 - regular graph </P> </Li> <Li> <P> 3 - regular graph </P> </Li> </Ul> <Li> <P> 0 - regular graph </P> </Li> <P> 0 - regular graph </P>

The number of the edges in a regular graph of degree d and n vertices is