A simple graph with 
graph vertices in which
each graph vertex has vertex
degree 
has a Hamiltonian cycle.
Dirac's Theorem
See also
Hamiltonian CycleExplore with Wolfram|Alpha
References
Dirac, G. "Some Theorems on Abstract Graphs." Proc. London Math. Soc. 2, 69-81, 1952.Li, H. "Generalizations of Dirac's Theorem in Hamiltonian Graph Theory--A Survey." Disc. Math. 313, 2034-2053, 2013.Referenced on Wolfram|Alpha
Dirac's TheoremCite this as:
Weisstein, Eric W. "Dirac's Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/DiracsTheorem.html