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Full friendly index sets of Cartesian products of two cycles

โœ Scribed by Wai Chee Shiu; Man Ho Ling

Publisher
Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society
Year
2010
Tongue
English
Weight
238 KB
Volume
26
Category
Article
ISSN
1439-7617

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๐Ÿ“œ SIMILAR VOLUMES

When the cartesian product of two direct
When the cartesian product of two directed cycles is hyperhamiltonian
โœ Joseph A. Gallian; David Witte ๐Ÿ“‚ Article ๐Ÿ“… 1987 ๐Ÿ› John Wiley and Sons ๐ŸŒ English โš– 149 KB

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, x Z, of two directed cycles is hyperhamiltonian if and only if there are positive integers rn and n with ma + nb

Disjoint circuits in the cartesian produ
Disjoint circuits in the cartesian product of two directed cycles
โœ Stephen Curran ๐Ÿ“‚ Article ๐Ÿ“… 1994 ๐Ÿ› John Wiley and Sons ๐ŸŒ English โš– 291 KB

## Abstract We show that the Cartesian product of two directed cycles __Z__~__a__~ X __Z__~__b__~ has __r__ disjointly embedded circuits __C__~1~, __C__~2~, โƒ›, __C__~r~ with specified knot classes knot__(C~i~) = (m~i~, n~i~)__, for __i__ = 1, 2, โƒ›, __r__, if and only if there exist relatively prime

Generalized hamiltonian circuits in the
Generalized hamiltonian circuits in the cartesian product of two-directed cycles
โœ Douglas S. Jungreis ๐Ÿ“‚ Article ๐Ÿ“… 1988 ๐Ÿ› John Wiley and Sons ๐ŸŒ English โš– 299 KB

We find necessary and sufficient conditions for the existence of a closed walk that traverses r vertices twice and the rest once in the Cayley digraph of 2, @ 2,. This is a generalization of the results known for r = 0 or 1. In 1978, Trotter and Erdos [3] gave a necessary and sufficient condition f

When the cartesian product of two direct
When the cartesian product of two directed cycles is hypo-Hamiltonian
โœ Laurence E. Penn; David Witte ๐Ÿ“‚ Article ๐Ÿ“… 1983 ๐Ÿ› John Wiley and Sons ๐ŸŒ English โš– 150 KB

We show that the Cartesian product Z, x Z, of two directed cycles is hypo-Hamiltonian (Hamiltonian) if and only if there is a pair of relatively prime positive integers m and n with ma + nb = ab -1 (ma + nb = ab). The result for hypo-Hamiltonian is new; that for Hamiltonian is known. These are speci