On the diameter of the Cayley Graph Hl,p

Resumo

The family H`;p has been de ned in the context of edge parti- tions. Subsequently, it was shown to be composed of Hamiltonian Cayley graphs, and that it is possible to determine the diameter of H`;p in O(`) time. The established properties such as the low di- ameter suggest the H`;p graph as a good topology for the design of interconnection networks. The p`􀀀1 vertices of the graph H`;p are the `-tuples with values between 0 and p 􀀀 1, such that the sum of the ` values is a multiple of p, and there is an edge between two ver- tices if the two corresponding tuples have two pairs of entries whose values di er by one unit. Our goal is to nd the diameter of Cayley graph H`;p in time O(log(`+p)). In this work, we did this for some families of graphs. We also show that the diameter of H`;p is the same of Hp;`. Finally, we nd a tight upper bound on the diameter of H`;p.

Descrição

Palavras-chave

Interconnection networks, Cayley graphs, Diameter and graphs Hl,p

Citação

CASTONGUAY, Daine; RIBEIRO, André da C.; KOWADA, Luis Antonio B.; FIGUEIREDO, Celina M. H. de. On the diameter of the Cayley Graph Hl,p. Matemática Contemporânea, Rio de Janeiro, v. 44, p. 1-10, 2015.