𝔖 Bobbio Scriptorium
✦   LIBER   ✦

The hamilton spaces of cayley graphs on abelian groups

✍ Scribed by Brian Alspach; Stephen C. Locke; Dave Witte

Publisher
Elsevier Science
Year
1990
Tongue
English
Weight
759 KB
Volume
82
Category
Article
ISSN
0012-365X

No coin nor oath required. For personal study only.

✦ Synopsis

The Hamilton cycles of a graph generate a subspace of the cycle space called the Hamilton space. The Hamilton space of any connected Cayley graph on an abelian group is determined in this paper.

πŸ“œ SIMILAR VOLUMES

Hamilton cycle and Hamilton path extenda
Hamilton cycle and Hamilton path extendability of Cayley graphs on abelian groups
✍ Ε tefko MiklaviČ; PrimoΕΎ Ε parl πŸ“‚ Article πŸ“… 2011 πŸ› John Wiley and Sons 🌐 English βš– 198 KB

## Abstract In this paper the concepts of Hamilton cycle (HC) and Hamilton path (HP) extendability are introduced. A connected graph Ξ“ is __n__‐__HC‐extendable__ if it contains a path of length __n__ and if every such path is contained in some Hamilton cycle of Ξ“. Similarly, Ξ“ is __weakly n__‐__HP‐

On the Isomorphisms of Cayley Graphs of
On the Isomorphisms of Cayley Graphs of Abelian Groups
✍ Yan-Quan Feng; Yan-Pei Liu; Ming-Yao Xu πŸ“‚ Article πŸ“… 2002 πŸ› Elsevier Science 🌐 English βš– 190 KB

Let G be a finite group, S a subset of G=f1g; and let Cay ðG; SÞ denote the Cayley digraph of G with respect to S: If, for any subset T of G=f1g; CayðG; SÞ ffi CayðG; T Þ implies that S a ¼ T for some a 2 AutðGÞ; then S is called a CI-subset. The group G is called a CIM-group if for any minimal gene

Hamiltonian decompositions of Cayley gra
Hamiltonian decompositions of Cayley graphs on Abelian groups
✍ Jiuqiang Liu πŸ“‚ Article πŸ“… 1994 πŸ› Elsevier Science 🌐 English βš– 606 KB

Alspach has conjectured that any 2k-regular connected Cayley graph cay(A,S) on a finite abelian group A can be decomposed into k hamiltonian cycles. In this paper, the conjecture is shown to be true if S= {sl,sz, s3} is a minimal generating set of A with 1 Al odd, or S={sl,s& . . . . sk} is a genera

Hamilton-Connected Cayley Graphs on Hami
Hamilton-Connected Cayley Graphs on Hamiltonian Groups
✍ Brian Alspach; Yusheng Qin πŸ“‚ Article πŸ“… 2001 πŸ› Elsevier Science 🌐 English βš– 109 KB

It is proven that every connected Cayley graph X , of valency at least three, on a Hamiltonian group is either Hamilton laceable when X is bipartite, or Hamilton connected when X is not bipartite.

Hamiltonian Decompositions of Cayley Gra
Hamiltonian Decompositions of Cayley Graphs on Abelian Groups of Odd Order
✍ Jiuqiang Liu πŸ“‚ Article πŸ“… 1996 πŸ› Elsevier Science 🌐 English βš– 380 KB

Alspach has conjectured that any 2k-regular connected Cayley graph cay(A, S) on a finite abelian group A can be decomposed into k hamiltonian cycles. In this paper, the conjecture is shown to be true if S=[s 1 , s 2 , ..., s k ] is a minimal generating set of an abelian group A of odd order (where a