Trivalent Cayley graphs for interconnection networks
β Scribed by Premkumar Vadapalli; Pradip K. Srimani
- Publisher
- Elsevier Science
- Year
- 1995
- Tongue
- English
- Weight
- 625 KB
- Volume
- 54
- Category
- Article
- ISSN
- 0020-0190
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## 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.
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,.
In this paper we deal with trivalent Cayley interconnection networks and we introduce a new representation of them emphasizing their geometric characteristics. Looking inside this model, a new shortest routing algorithm is derived. @ 1997 Elsevier Science B.V.
Interconnection networks require dense graphs in the sense that many nodes with relatively few links may be connected with relatively short paths. Some recent constructions of such dense graphs with a given maximal degree A and diameter D (known as (A, D) graphs) are reviewed here. The paper also co