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When the cartesian product of two directed cycles is hyperhamiltonian
Author(s) -
Gallian Joseph A.,
Witte David
Publication year - 1987
Publication title -
journal of graph theory
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 54
eISSN - 1097-0118
pISSN - 0364-9024
DOI - 10.1002/jgt.3190110105
Subject(s) - cartesian product , combinatorics , digraph , mathematics , vertex (graph theory) , product (mathematics) , cartesian coordinate system , discrete mathematics , graph , geometry
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 Z a × Z b 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 Z a × Z b .