Superfluous edges and exponential expansions of De Bruijn and Kautz graphs

Abstract

A new way to expand De Bruijn and Kautz graphs is presented. It consists of deleting superfluous sets of edges (i.e., those whose removal does not increase the diameter) and adding new vertices and new edges preserving the maximum degree and the diameter. The number of vertices added to the Kautz graph, for a fixed maximum degree greater than four, is exponential on the diameter. Tables with lower bounds for the order of superfluous sets of edges and the number of vertices that can be added, are presented.