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Hamiltonian paths in Cayley digraphs of finitely-generated infinite abelian groups

โœ Scribed by Douglas Jungreis

Publisher
Elsevier Science
Year
1989
Tongue
English
Weight
983 KB
Volume
78
Category
Article
ISSN
0012-365X

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โœฆ Synopsis

We show every finitely-generated, infinite abeliar_ group (i.e. Zn x G where G is a finite abelian group) has a minimal generating set for which the Cayley digraph has a two-way in&rite hamiltonian path, and if n 2 2, then this Cayley digraph also has a one-way infinite hamiltonian path. We show further that in the case of Z" (n 3 2), the Cayley digraph is 2-ply hamiltonian.

๐Ÿ“œ SIMILAR VOLUMES

Infinite Hamiltonian paths in Cayley dig
Infinite Hamiltonian paths in Cayley digraphs
โœ Irwin L Jungreis ๐Ÿ“‚ Article ๐Ÿ“… 1985 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 942 KB

Let Cay(S : H) be the Cayley digraph of the generators S in the group H. A one-way infinite Hamiltonian path in the digraph G is a listing of all the vertices [q: 1 ~< i <oo], such that there is an arc from vi to vi+ 1. A two-way infinite Hamiltonian path is similarly defined, with i ranging from -0

Circuits in cayley digraphs of finite ab
Circuits in cayley digraphs of finite abelian groups
โœ Anne Marie Wilkinson ๐Ÿ“‚ Article ๐Ÿ“… 1990 ๐Ÿ› John Wiley and Sons ๐ŸŒ English โš– 290 KB

## Abstract We find all possible lengths of circuits in Cayley digraphs of twoโ€generated abelian groups over the twoโ€element generating sets and over certain threeโ€element generating sets.

Digraphical Regular Representations of I
Digraphical Regular Representations of Infinite Finitely Generated Groups
โœ R.G. Mรถller; N. Seifter ๐Ÿ“‚ Article ๐Ÿ“… 1998 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 104 KB

A directed Cayley graph X is called a digraphical regular representation (DRR) of a group G if the automorphism group of X acts regularly on X . Let S be a finite generating set of the infinite cyclic group Z. We show that a directed Cayley graph X (Z, S) is a DRR of Z if and only if As a general r