Constructing a Series of Families of Degree Six Circulant Networks
Emilia A. Monakhova, Oleg G. Monakhov · Journal of Applied and Industrial Mathematics · 2022
Abstract We consider a solution of the problem of constructing a series of families of circulant networks of degree six specified analytically with the help of two parameters one of which is the network diameter. Based on the analysis and generalization of the properties of a new description of an extremal family of circulants, a general series of families of circulant graphs of degree six of arbitrary diameters is constructed that includes extremal circulant graphs of degree six and new infinite families of circulants with an even number of vertices. In the found series of families, descriptions of a series of circulant graphs of any given diameter are analytically determined. Optimality ranges of series graphs are algorithmically identified, where ‘optimal’ is understood as a circulant graph of degree six with the minimum possible diameter for a given number of vertices. The resulting series of families of circulant networks is promising as a scalable topology model for networks on a chip.