## Abstract In this paper the concepts of Hamilton cycle (HC) and Hamilton path (HP) extendability are introduced. A connected graph Ξ is __n__β__HCβextendable__ 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__β__HPβ
Hamilton cycles in Trivalent Cayley graphs
β Scribed by Meghanad D. Wagh; Jiancheng Mo
- Publisher
- Elsevier Science
- Year
- 1996
- Tongue
- English
- Weight
- 455 KB
- Volume
- 60
- Category
- Article
- ISSN
- 0020-0190
No coin nor oath required. For personal study only.
β¦ Synopsis
It is shown that the Trivalent Cayley graphs, TC,,, are near recursive. In particular, TC, is a union of four copies of i"Cn_2 with additional well placed nodes. This allows one to recursively build the Hamilton cycle in TC,.
π SIMILAR VOLUMES
## 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
## UNIVERSIW OF WATERLOO ' The research reported here has been sponsored by the Canadian Commonwealth Association.
## Abstract If __n__ is divisible by at least three distinct primes, the dihedral group __D~n~__ can be generated by three nonredundant, involuntary elements. We study the Cayley graphs resulting from such a presentation of __D~n~__ for several families of __n__ and for all admissible __n__ < 120.