有向圈码  

Directed Cycle Code

作　　者：赵颖 王燕[1] ZHAO Ying;WANG Yan(School of Mathematics and Information Sciences,Yantai University,Yantai 264005,China)

机构地区：[1]烟台大学数学与信息科学学院,山东烟台264005

出　　处：《烟台大学学报（自然科学与工程版）》2023年第4期379-383,392,共6页Journal of Yantai University(Natural Science and Engineering Edition)

基　　金：山东省自然科学基金资助项目(ZR2020MA044)。

摘　　要：有向图的有向圈码是一个可以控制有向图所有顶点的长度最小的一个有向圈。本文定义了有向图的有向圈码,并且给出了有向圈码和有向图覆盖之间的关系。在凯莱有向图中,研究了一个有向圈是有向圈码的充分必要条件。特别地,在凯莱有向图中,一个循环子群决定一个有向圈码的充分必要条件是这个图的凯莱子集既是这个子群的一个左陪集代表系也是一个右陪集代表系。A directed cycle code of a digraph is a smallest directed cycle that controls all vertices of the digraph.The directed cycle codes of digraphs are defined in this paper,and the relation between the directed cycle codes and the covers of digraphs are given.In Cayley digraphs,necessary and sufficient conditions for a directed cycle to be a directed cycle code are listed out.In particular,a necessary and sufficient condition for a cyclic subgroup to determine a directed cycle code is that the Cayley subset of this graph is both a left and a right coset representative of this subgroup.

关 键 词：有向圈码 覆盖 有向凯莱图 

分 类 号：O157.6[理学—数学]