When the cartesian product of two directed cycles is hyperhamiltonian
Joseph A. Gallian, David S. Witte · Journal of Graph Theory · 1987
Abstract We say a digraph G is hyperhamiltonian if there is a spanning closed walk in G which passes through one vertex exactly twice and all others exactly once. We show the cartesian product Za × Zb of two directed cycles is hyperhamiltonian if and only if there are positive integers m and n with ma + nb = ab + 1 and gcd(m, n) = 1 or 2. We obtain a similar result for the vertex‐deleted subdigraphs of Za × Zb.