A finite connected graph G is called square-Hamiltonian if G2 is Hamiltonian. We prove that any join of the family of Hamiltonian graphs by tree is square-Hamiltonian.
Applying this statement we show that the line graph and any round-about reconstruction of an arbitrary finite connected graph is square-Hamiltonian.
Description:
On square-Hamiltonian graphs / K. D. Protasova // Algebra and Discrete Mathematics. - 2005. - № 3. - 56-59.
