When the cartesian product of two directed cycles is hyperhamiltonian

Joseph A Gallian, David Witte

Research output: Contribution to journalArticlepeer-review

6 Scopus citations

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.

Original languageEnglish (US)
Pages (from-to)21-24
Number of pages4
JournalJournal of Graph Theory
Volume11
Issue number1
DOIs
StatePublished - Jan 1 1987

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