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
Large Cayley graphs on an abelian group
β Scribed by C. Garcia; C. Peyrat
- Publisher
- Elsevier Science
- Year
- 1997
- Tongue
- English
- Weight
- 525 KB
- Volume
- 75
- Category
- Article
- ISSN
- 0166-218X
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β¦ Synopsis
In this paper we determine new bounds on the maximum number of vertices of a Cayley graph with fixed diameter and degree on an abelian group.
π SIMILAR VOLUMES
Let G be a finite group, S a subset of G=f1g; and let Cay Γ°G; SΓ denote the Cayley digraph of G with respect to S: If, for any subset T of G=f1g; CayΓ°G; SΓ ffi CayΓ°G; T Γ implies that S a ΒΌ T for some a 2 AutΓ°GΓ; then S is called a CI-subset. The group G is called a CIM-group if for any minimal gene
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.
A graph G is 2-extendable if any two independent edges of G are contained in a perfect matching of G. A Cayley graph of even order over an abelian group is 2-extendable if and only if it is not isomorphic to any of the following circulant graphs: (I) Z2.(1,2n -1), n >~ 3; (II) ZE.(1,2,2n -1,2n -2),