𝔖 Bobbio Scriptorium
✦   LIBER   ✦

The exponent of Cartesian product of cycles

✍ Scribed by Byeong Moon Kim; Byung Chul Song; Woonjae Hwang

Book ID
108052425
Publisher
Elsevier Science
Year
2009
Tongue
English
Weight
314 KB
Volume
22
Category
Article
ISSN
0893-9659

No coin nor oath required. For personal study only.

πŸ“œ SIMILAR VOLUMES

When the cartesian product of directed c
When the cartesian product of directed cycles is Hamiltonian
✍ William T. Trotter Jr.; Paul ErdΓΆs πŸ“‚ Article πŸ“… 1978 πŸ› John Wiley and Sons 🌐 English βš– 225 KB

The Cartesian product of two hamiltonian graphs is always hamiltonian. For directed graphs, the analogous statement is false. We show that the Cartesian product C,,, x C, , of directed cycles is hamiltonian if and only if the greatest common divisor (g.c.d.) d of n, and n, is a t least two and there

Dominating Cartesian products of cycles
Dominating Cartesian products of cycles
✍ Sandi KlavΕΎar; Norbert Seifter πŸ“‚ Article πŸ“… 1995 πŸ› Elsevier Science 🌐 English βš– 578 KB
When the cartesian product of two direct
When the cartesian product of two directed cycles is hyperhamiltonian
✍ Joseph A. Gallian; David Witte πŸ“‚ Article πŸ“… 1987 πŸ› John Wiley and Sons 🌐 English βš– 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
✍ Stephen Curran πŸ“‚ Article πŸ“… 1994 πŸ› John Wiley and Sons 🌐 English βš– 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~, ⃛, __C__~r~ with specified knot classes knot__(C~i~) = (m~i~, n~i~)__, for __i__ = 1, 2, ⃛, __r__, if and only if there exist relatively prime