De Bruijn Digraphs, Kautz Digraphs, and Their Generalizations

An interesting problem in network designs is as follows: Given natural numbers n and d, find a digraph (directed graph) with n vertices, each of which has outdegree at most d, to minimize the diameter and to maximize the connectivity. This is a multiobjective optimization problem. Usually, for such a problem, solution is selected based on tradeoff between two objective fuctions. However, for this problem, it is different; that is, there exists a solution which is optimal or nearly optimal to both. Such a solution comes from study of de Bruijn digraphs, Kautz digraphs, and their generalizations. In this chapter, we introduce and survey results on these subjects.

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