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
A non-Cayley-invariant Cayley graph of the elementary Abelian group of order 64
β Scribed by Lewis A. Nowitz
- Publisher
- Elsevier Science
- Year
- 1992
- Tongue
- English
- Weight
- 392 KB
- Volume
- 110
- Category
- Article
- ISSN
- 0012-365X
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β¦ Synopsis
We construct a degree 32 Cayley graph whose automorphism group contains two nonconjugate regular subgroups isomorphic to Z$
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.
In this paper it is shown that every connected Cayley graph of a semt-direct product of a cyclic group of prime order by an abelian group is hamiltonian. In particular, every connected Cayley graph of a group G is hamiltonian provided that G is of order greater than 2 and it contains a normal cyclic
This paper completes the determination of all integers of the form pqr (where p, q, and r are distinct primes) for which there exists a vertex-transitive graph on pqr vertices which is not a Cayley graph.