The cube of every connected graph is 1-hamiltonian
Gary Chartrand, Sanjiv Kapoor · Journal of Research of the National Bureau of Standards Section B Mathematical Sciences · 1969
Let G be any connected graph on 4 or more points.The graph G3 has as it s point set that of C, and two distinct pointE U and v are adjacent in G3 if and only if the distance be twee n u and v in G is at most three.It is shown that not only is G" hamiltonian , but the removal of any point from G" still yields a hamiltonian graph.