On the Structure of G(H, k)

• 作者: Guixin Deng Pingzhi Yuan
• 来源期刊: 代数集刊:英文版
• 学科: 数学
• 关键词: 结构 顶点集 阿贝尔群 正整数 有向图 GCD P-群 H2
• 年，卷（期）: 2014,（2）
• 页码范围: 317-330
• 页数: 14页
• 分类号: O157.5
• 语种: 中文

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.