Chordal Topologies for Interconnection Networks

The class of dense circulant graphs of degree four with optimal distance-related properties is analyzed in this paper. Two geometric characterizations are given, one in the plane and other in the space. Both characterizations facilitate the analysis of their topological properties and corroborate their suitability for implementing interconnection networks for distributed and parallel computers. Also, a distance-hereditary non-disjoint decomposition of these graphs into rings is computed. Besides its practical consequences, this decomposition allows us the presentation of these optimal circulant graphs as a particular evolution of the traditional ring topology.