The directed genus of the de Bruijn graph

被引：3

作者：

Hales, Alfred W. ^{[1
]}

Hartsfield, Nora ^{[2
]}

机构：

[1] Ctr Commun Res, San Diego, CA 92121 USA

[2] Western Washington Univ, Dept Math, Bellingham, WA 98225 USA

来源：

DISCRETE MATHEMATICS | 2009年 / 309卷 / 17期

关键词：

Directed genus; de Bruijn graph; Directed embeddings; de Bruijn sequence invariant;

D O I：

10.1016/j.disc.2007.11.003

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Define the directed genus, Gamma(G), of an Eulerian digraph G to be the minimum value of p for which G has a 2-cell embedding in the orientable surface of genus p so that every face of the embedding is bounded by a directed circuit in G. The directed genus of the de Bruijn graph D-n is shown to be Gamma(D-n) = 2(n-1) + 1 - 1/2(n + 2) Sigma(d vertical bar n+2) phi(d)2(n+2/d). (C) 2007 Elsevier B.V. All rights reserved.

引用

页码：5259 / 5263

页数：5

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