Triple-loop networks with arbitrarily many minimum distance diagrams

Details Triple-loop networks with arbitrarily many minimum distance diagrams Triple-loop networks with arbitrarily many minimum distance diagrams

2007-05-24

arxiv.org/abs/0705.3631v1

Discrete Mathematics, 309(6), April 2009, 1672-1684.

Mathematics

Combinatorics

17 pages, 8 figures

Scientific paper

10.1016/j.disc.2008.02.047

Minimum distance diagrams are a way to encode the diameter and routing information of multi-loop networks. For the widely studied case of double-loop networks, it is known that each network has at most two such diagrams and that they have a very definite form "L-shape''. In contrast, in this paper we show that there are triple-loop networks with an arbitrarily big number of associated minimum distance diagrams. For doing this, we build-up on the relations between minimum distance diagrams and monomial ideals.

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