Left loops, bipartite graphs with parallelism and bipartite involution sets

被引：4
|
作者：
Karzel, H [1 ]
Pianta, S
机构：
[1] Tech Univ Munich, Zentrum Math, D-80290 Munich, Germany
[2] Univ Cattolica, Dipartimento Matemat & Fis, I-25121 Brescia, Italy
来源：
ABHANDLUNGEN AUS DEM MATHEMATISCHEN SEMINAR DER UNIVERSITAT HAMBURG | 2005年 / 75卷 / 1期
关键词：
graphs; loops; involution sets;
D O I：
10.1007/BF02942043
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We describe a representation of any semiregular left loop by means of a semiregular bipartite involution set or, equivalently, a 1-factorization (i.e., a parallelism) of a bipartite graph, with at least one transitive vertex. In these correspondences, Bol loops are associated on one hand to invariant regular bipartite involution sets and, on the other hand, to trapezium complete bipartite graphs with parallelism; K-loops (or Bruck loops) are further characterized by a sort of local Pascal configuration in the related graph.
引用
收藏
页码：203 / 214
页数：12
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