Classification of nonorientable regular embeddings of complete bipartite graphs

被引：14
作者：
Kwak, Jin Ho [1 ]
Kwon, Young Soo [2 ]
机构：
[1] Pohang Univ Sci & Technol, Dept Math, Pohang 790784, South Korea
[2] Yeungnam Univ, Dept Math, Kyongsan 712749, South Korea
来源：
JOURNAL OF COMBINATORIAL THEORY SERIES B | 2011年 / 101卷 / 04期
关键词：
Graph; Surface; Regular embedding; Regular map; N-DIMENSIONAL CUBES; POWER; MAPS;
D O I：
10.1016/j.jctb.2011.03.003
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
A 2-cell embedding of a graph G into a closed (orientable or nonorientable) surface is called regular if its automorphism group acts regularly on the flags - mutually incident vertex-edge-face triples. In this paper, we classify the regular embeddings of complete bipartite graphs K-n,K-n into nonorientable surfaces. Such a regular embedding of K-n,K-n exists only when n is of the form n = 2p(1)(a1) p(2)(a2) ... p(k)(ak) where the p(i) are primes congruent to +/- 1 mod 8. In this case, up to isomorphism the number of those regular embeddings of K-n,K-n is 2(k). (C) 2011 Elsevier Inc. All rights reserved.
引用
收藏
页码：191 / 205
页数：15
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