Robert Lewis - Academia.edu (original) (raw)
Uploads
Papers by Robert Lewis
We consider the degree-diameter problem for undirected and directed circulant graphs. To date, at... more We consider the degree-diameter problem for undirected and directed circulant graphs. To date, attempts to generate families of large circulant graphs of arbitrary degree for a given diameter have been concentrated mainly on the diameter 2 case. We give new constructions which improve the current best known asymptotic orders for every diameter, and we present a revised table of largest known circulant graphs of small degree and diameter. As an application, we show how our constructions in the directed case can be used to obtain upper bounds on the minimum size of a set A ⊆ Zn such that the k-fold sumset kA is equal to Zn.
We consider the degree-diameter problem for undirected and directed circulant graphs. To date, at... more We consider the degree-diameter problem for undirected and directed circulant graphs. To date, attempts to generate families of large circulant graphs of arbitrary degree for a given diameter have been concentrated mainly on the diameter 2 case. We give new constructions which improve the current best known asymptotic orders for every diameter, and we present a revised table of largest known circulant graphs of small degree and diameter. As an application, we show how our constructions in the directed case can be used to obtain upper bounds on the minimum size of a set A ⊆ Zn such that the k-fold sumset kA is equal to Zn.