Let G be a group generated by X. A Cayley graph ouer G is defined as a graph G(X) whose vertex set is G and whose edge set consists of all unordered pairs [a, b] with a, b E G and am'b E X U X-', where X-t denotes the set (x-t ( .x E X}. When X is a minimal generating set or each element of X is of
On edge-hamiltonian Cayley graphs
β Scribed by Ulrike Baumann
- Publisher
- Elsevier Science
- Year
- 1994
- Tongue
- English
- Weight
- 667 KB
- Volume
- 51
- Category
- Article
- ISSN
- 0166-218X
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π SIMILAR VOLUMES
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.
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
## Abstract A group Ξ is said to possess a hamiltonian generating set if there exists a minimal generating set Ξ for Ξ such that the Cayley color graph __D__~Ξ~(Ξ) is hamiltonian. It is shown that every finite abelian group has a hamiltonian generating set. Certain classes of nonabelian groups are