On the Structure of G（H, k）  

作　　者：Guixin Deng Pingzhi Yuan 

机构地区：[1]School of Mathematical Sciences, Guangxi Teachers Education University Nanning 530023, China [2]School of Mathematics, South China Normal University Guangzhou 510631, China

出　　处：《Algebra Colloquium》2014年第2期317-330,共14页代数集刊（英文版）

基　　金：Supported by NSF of China （Grant No. 11271142） and the Guangdong Provincial Natural Science Foundation （Grant No. $2012010009942）.

摘　　要：Let H be an abelian group written additively and k be a positive integer. Let G（H,k） denote the digraph whose set of vertices is just H, and there exists a directed edge from a vertex a to a vertex b if b = ka. In this paper we give a necessary and sumcient condition for G（H, k1） ≈ G（H, k2）. We also discuss the problem when G（H1, k） is isomorphic to G（H2, k） for a given k. Moreover, we give an explicit formula of G（H, k） when H is a p-group and gcd（p, k） = 1.Let H be an abelian group written additively and k be a positive integer. Let G（H,k） denote the digraph whose set of vertices is just H, and there exists a directed edge from a vertex a to a vertex b if b = ka. In this paper we give a necessary and sumcient condition for G（H, k1） ≈ G（H, k2）. We also discuss the problem when G（H1, k） is isomorphic to G（H2, k） for a given k. Moreover, we give an explicit formula of G（H, k） when H is a p-group and gcd（p, k） = 1.

关 键 词：DIGRAPH COMPONENT CYCLE HEIGHT 

分 类 号：O157.5[理学—数学] O152.2[理学—基础数学]