Cayley line graphs of transitive groupoids

Miskolc Mathematical Notes

article

Nándor Sieben¹ 

[1] Department of Mathematics and Statistics, Northern Arizona University

关键词: groupoid;    line graph;    Cayley color graph;    partial automorphism;    semidirect product;   

DOI  :  10.18514/MMN.2023.1651

学科分类：数学（综合）

来源: Miskolci Egyetem

【 摘 要 】

A groupoid is a small category with inverses. Adding appropriate colors to the edges of the line graph of a transitive groupoid creates a Cayley line graph of the groupoid. The groupoid of partial automorphisms of the Cayley line graph is isomorphic to a semidirect product of the original groupoid. Using the trivial coloring to build the Cayley line graph makes the semidirect product trivial, hence the groupoid of partial automorphisms of this Cayley line graph is isomorphic to the original groupoid.

【 授权许可】

CC BY